In an earlier thread, I have a mod warning and a series of follow-up answers that address at least some of your questions.

Yes, a mod warning, really:

~~

Hi, friends,

AskHistorians is a subreddit where people with questions about history can get answers from those with expert-level knowledge in the topic at hand.

We do not allow answers from those who

make up false tales and make themselves into fools

when they have the wit and the will to do the work if they wished

And for those posting one-line jokes and complaints,

acting like fools and performing jests

against the laws of our lord...

saying mean things and mockeries against those who give them no gifts

(William Langland, 'Piers Plowman', late 14th century)

You may well find yourself treated like Borra the Fool in 1414, who, as the target of a jest, was suddenly hoisted into the air by a costumed Grim Reaper--at which point, terrified, he urinated all over the Aragonese courtiers.

Thanks!

For those that are waiting with anticipation for an in-depth answer, you might find prior questions and responses relevant to your interests about daily life and their respectability, both courtesy of /u/texpeare.

So I will start by saying this question is too broad to be addressed by any single response. This is because a) the position and duties varied slot across geographic areas in Europe b) the time period of "middle ages" is too broad as the profession evolved. So I'll start with a brief history and how it eventually ended up. This will specifically detail fools according to the English, Irish, and Scottish traditions. These two are great showcases for the two prominent traditions of the British Isles.

In England, the fool can be traced to France. The initial position was that of troubadors. The were itinerant preformers that would often exchange entertainment for food and/or lodging. Additionally, they depending on their skills would be asked to preform at events and for prominent individuals. These troubadors usually travelled in groups and they wandered about. This position eventually changed as the tastes of their audiences changed. As acrobatics began to fall out of fashion epic ballads and epics came into fashion with accompanying music preformed by bards, such as the Song of Roland and Tristan and Iseult. These long ballads and epics required long hours of composition. As such it came to be fashionable to hire bards to compose and preform for wealthy individuals.

This is the point in which it crosses to the Isles. As the Battle of Hastings brought Norman control to Britain, and the French tastes and courtly expectations came with them. The bards that came to entertain in courts were usually not very well off and were able to make names for themselves based on patronage. Enter Eleanor of Aquitaine, Queen Consort of France and England. In her own right she was a duchess and incredibly wealthy. She used her money to support the arts in an unheard of way.

Inspired by Eleanor many wealthy young women and men began to feel passionately for the arts with both genders beginning to compose new ballads. Then the point shifted. The ballads became satire. They often poked fun at local lords and they became utterly inundated with "in" jokes to the point that today many make absolutely no sense! Eventually the ballads were dispensed with entirely and the satire remained. While the fool who did acrobatics and hurt himself for humor was never common, a respected satirist was indeed a fool. They (as they could be either gender) pointed out flaws and was able to make people laugh through with was. These insights made them invaluable in the court. These individuals were educated, typically wealthy, and often related to members of the court.

This contrasts greatly to the Irish and Scottish traditions! Firstly I'll say that a musical tradition of itinerant storytellers was strong in Ireland. It continued well into the British conquest with many of the tales being written down and some even available as myths to this day. This is not important in this discussion though. What matters here is the Vikings! The Viking tradition featured and relied heavily on scops. So when the Vikings conquered in Scotland, Ireland, and yes even England they brought this tradition with them.

Now scops were different than troubadors. They were usually generational, in that their trade was passed father to son down the generations. They were almost always attached to specific families and existed to provide an oral history of the deeds and lineage of the family that supported them. These were often encoded musically and we're preformed regularly. They acted as guides on important matters and were consulted as to see methods of governance that had happened in the past and how they turned out. This they were able to be historical advisors and influence everything from governance to marriages and inheritance. The tradition of scops while highly respected lasted in the Hebrides until the last Lord of the Isles fell, but on the mainland of Ireland the tradition died early following a conquest of the British and in the Scottish mainland it ended as the French and Scots participated in the Seann-chaidreachas or the "Auld Alliance" in the late 13th century. As the French court came to power the tradition of musical advising via scops came to die out (it did remain in the highlands for some time) and the French tradition of bards came to the fore front.