Ahfpqyg

This goes back to Frederick Barbarossa. He granted the university the so called scholar's privilege the privilegium scholasticum or authentica habita in 1150s. Full universities had to be granted papal or princely privileges to be founded but from 1150s on they had judicial autonomy. It was the result of active and collective defiance of students and professors against infringements and incursions. As Bologna was the blueprint for all European Universities, this was a guiding principle for all of them. Per the will of Barabrossa it also found entry into the Corpus iuris civilis and was later confirmed by pope Alexander III or the French king in 1200. Later re-affirmations were necessary. Like the papal bull Parens scientiarum in 1231 or when the students in Oxford went on strike after the Saint scholastica riots.

Authentica habita

Authentica habita, or Privilegium Scholasticum, was a document written in 1155 ca. by the Emperor Frederick I Barbarossa. In it, he set out for the first time some of the rules, rights and privileges of Universities. It is a key founding document in the history of the medieval university in Europe.

Scholars from all over Europe had begun to travel to Bologna to study civil and canon law, and newly rediscovered works of Roman law, from the mid-11th century. As foreigners there, they found themselves without legal protection. A particular difficulty was the practice of the Right of Reprisal, where their property could be seized on foot of debts incurred by their countrymen.

The document grants several rights and protections to scholars including:

• Similar immunities and freedoms as those held by the clergy, provided they conformed to certain attributes, such as clerical dress;
• Freedom of movement and travel for the purposes of study;
• Immunity from the right of reprisal; and
• The right to be tried by their masters, or the Bishops court, rather than local civil courts.

The document was subsequently confirmed by Pope Alexander III. The Emperor incorporated the document into Justinian’s Codex, the extant body of Roman law, indicating its significance.

More on this Pearl Kibre: "Scholarly privileges in the Middle Ages; the rights, privileges, and immunities of scholars and universities at Bologna, Padua, Paris, and Oxford", Cambridge, 1962.

Going back to the subquestions:

1. This is much more than just a 'right to asylum'. It is a quite extensive set of rights and privileges that come with legal autonomy.

2. Throughout the middle ages European universities had these rights and should they come under fire – which they did almost regularly – they rigorously defended their rights. But almost needless to say, as the question already states that they were 're-instated in Greece', together with the advent of modern states in early modern times the privileges were under constant erosion. Today, only remnants of this Academic freedom remain. And those are still under constant attack.

3. European universities in general do not prefer to keep their own police force. They typically do not have anything like a police force, at most only a small (private) security force, turning of the lights or keeping watch. American campus police is a whole different story.

As an illustration for how far reaching this legal autonomy was, a few highlights that show that unlike Islamic palace schools (PDF) punishments stopped short before death penalty, but were certainly sometimes bizarre in the eyes of modern readers. Killing a person in the street seems to have been punished in any case, but much less sever if you were a student. A student on the other hand that allowed himself being caught talking English – of all causes…:

In the universities of Southern France, the marriage of resident doctors and students was also contemplated, and the statutes of the University of Aix contain a table of charges payable as "charivari" by a rector, a doctor, a licentiate, a bachelor, a student, and a bedel. In each case the amount payable for marrying a widow was double the ordinary fee. If the bridegroom declined to pay, the "dominus promoter," accompanied by "dominis studentibus," was, by permission of the Rector, to go to his house armed with frying-pans, bassoons, and horns, and to make a great tumult, without, however, doing any injury to his neighbours. Continued recusancy was to be punished by placing filth outside the culprit's door on feast-days. […]

For contumacy, for grave moral offences, for crimes of violence, and for heresy, the penalty was expulsion. Less serious offences were punished by subtraction of "commons" i.e. deprivation of allowances for a day or a week (or longer), or by pecuniary fines. When College founders provided clothes as well as board and lodging for their scholars, the forfeiture of a robe took its place among the penalties with which offenders were threatened. The "poor boys" who sang in Chapel and waited on the Fellows were whipped like boys elsewhere, who were being taught grammar, but the birch was unknown as a punishment for undergraduates till late in the middle ages.

The introduction of corporal punishment into college life in England may be traced by a comparison of William of Wykeham's statutes with those of Henry VI. The King's College statute "De correctionibus faciendis circa delicta leviora" is largely a transcript of a New College statute, with the same title, and both contemplate subtraction of commons as the regular penalty. But the King's College statute contains an additional clause, to the effect that scholars and younger Fellows may be punished with stripes. In the statutes of Magdalen, dated some seventeen years later, William of Waynflete returned to the New College form of the statute, but he provided that his demys (i.e. scholars who received half the commons of a Fellow) should be subject to the penalty of whipping in the Grammar School.

The statutes of Christ's College prescribe a fine of a farthing for unpunctuality on the part of the scholars studying in the Faculty of Arts, and heavier fines for absence, and it is added that if the offender be not an adult, a whipping is to be substituted for the pecuniary penalty. At Brasenose, where the Fellows were all of the standing of at least a Bachelor of Arts, the undergraduate scholars were subjected to an unusually strict discipline, and offenders were to be punished either by fines or by the rod, the Principal deciding the appropriate punishment in each case.

For unpunctuality, for negligence and idleness, for playing, laughing, talking, making a noise or speaking English in a lecture-room, for insulting fellow- students, or for disobedience to his pastors and masters, the Brasenose undergraduate was to be promptly flogged. Among the crimes for which the birch is ordered we find " making odious comparisons," a phrase which throws some light on the conversational subjects of sixteenth-century undergraduates. The kind of comparison is indicated in the statute; remarks about the country, the family, the manners, the studies, and the ability, or the person, of a fellow-student must be avoided.

Similarly, at Jesus College, Cambridge, it is forbidden to compare country to country, race to race, or science to science, and William of Wykeham and other founders had to make similar injunctions. The medieval student was distinctly quarrelsome, and such records as the famous Merton "scrutiny" of 1339, and investigations by College Visitors, show that the seniors set the undergraduates a bad example. The statutes of Corpus Christi College, Oxford, provide for two new penalties. An offending undergraduate might be sentenced to feed by himself, at a small table in the middle of the Hall, and in aggravated cases to the monastic penalty of bread and water. An alternative penalty was detention in the library at the most inconvenient time ("per horam vel horas cum minime vellet"), and the performance of an imposition to be shown up in due course. The rough and ready penalty of the birch is, however, frequently mentioned in the statutes of Corpus and of other sixteenth-century Colleges. Cardinal Wolsey thought it proper that an undergraduate should be whipped until he had completed his twentieth year. At Trinity, Cambridge (where offenders were sociably flogged before the assembled College on Friday evenings) the age was eighteen. Dr Caius restricted the rod to scholars who were not adult. "We call those adults," he says, "who have completed their eighteenth year. For before that age, both in ancient times and in our own memory, youth was not accustomed to wear braccas, being content with tibialia reaching to the knees." The stern disciplinarian might find an excuse for prolonging the whipping age in the Founder's wish that, "years alone should not make an adult, but along with years, gravity of deportment and good character."

The leniency of the punishments for grave moral offences, as contrasted with the strict insistance upon the lesser matters of the law, cannot fail to impress modern readers, but this is not a characteristic peculiar to Leipsic. Fines, and in the fifteenth and sixteenth centuries, whippings were frequently inflicted in all universities for violent attacks upon the person. Dr Rashdall quotes a case at Ingolstadt where a student who had killed another in a drunken bout was let off with the confiscation of his goods, and the penalty of expulsion was remitted ; and the eighteenth-century history of Corpus Christi College at Oxford supplies more recent instances of punish- ments which could scarcely be said to fit the crime. The statutes of the French universities outside Paris and of the three medieval Scottish universities (St Andrews, Glasgow, and Aberdeen) supply many illustrations of the regulations we have noted elsewhere, but contain little that is unusual. St Andrews, which allowed hawking, forbade the dangerous game of football. The Faculty of Arts at Glasgow in 1532 issued an edict which has a curious resemblance to the Eton custom of "shirking." Reverence and filial fear were so important, said the masters, that no student was to meet the Rector, the Dean, or one of the Regents openly in the streets, by day or by night; immediately he was observed he must slink away and escape as best he could, and he must not be found again in the streets without special leave. The penalty was a public, flogging. Similarly, even a lawful game must not be played in the presence of a regent. Flogging was a recognised penalty in all the Scottish universities; it found its way into the system at St Andrews and Glasgow, and was introduced at once at Aberdeen. …
_{–– Robert S. Rait: "Life in the Medieval University", Cambridge Manuals of Science and Literature, Cambridge University Press: London, 1912. (Luckily, old enough to be on archive.org in full)}