The Lateran IV council in 1215 mentioned in the first post /u/searocksandtrees provided is one of the more solid points we have in terms of providing information on church attendance among the poor, particularly the rural poor. The mandate of yearly attendance, confession, and eucharist probably means that most people were not going to church once a year in 1215.

Most of the evidence for church attendance and involvement that we have comes from the towns - I don't know how you mean to define "peasants", so this may or may not pertain to your question. In towns, particularly following Lateran IV, there are not only reports of people attending mass daily, but attending multiple masses each day. It became a fairly common belief that the greatest point of spiritual efficacy in the mass was the actual raising and blessing of the Host (the bread), so you actually had groups of women (this sort of behavior was disproportionately female) running around to a whole bunch of churches to see as many elevations of the host as possible.

There was an intense sense of belonging and pride in high to late medieval town churches. There is no systematic study of this for the entirety of Europe, but Katherine French's The People of the Parish is a great case study of 15th century England.

For your specific questions:

Would the peasants attend mass regularly?

There's reason to believe the once a year rule was effective, but there are no hard numbers. Before Lateran IV we assume average attendance was less frequent.

Would they be expected to tithe?

Absolutely. The parish priest's income depended on this.

Would they have known their local priests,

It depends on where they lived. Small town or rural parish? Yes. Big city? Probably not.

and expected visits from priests to sick and dying family members?

Yes. Extreme unction was considered a necessary sacrament.

I have heard that in many areas, peasants tended to believe a mix of Christianity and more traditional beliefs (dragons and witches and such)

This is kind of a dangerous conceptual road to start down. There are certainly examples where high ecclesiastics are very irritated about lay superstition (Stephen de Bourbon's story of St. Guinefort comes to mind), but it would be unwise to suggest that even the great theologians did not believe in "dragons and witches and such." The gap between "high" and "low" piety is much smaller than is usually imagined.

I also know that mass was given in Latin in Europe, which most peasants wouldn't have known.

While true, this does not necessarily mean that people wouldn't have understood. Latin was intelligible to Italian speakers until the thirteenth century, and we have a lot of evidence that people were quite aware of what was going on both in the mass itself and in general principles of theology and canon law more generally. One of the most well-known examples is that during the trial of Joan of Arc, Joan is very obviously completely aware of several apparently cunning traps designed to ensnare her in a declaration of heresy.

I know nothing of Byzantine spirituality.

hi! hopefully your post will attract other responses, but just wanted to give you links to a couple of interesting earlier posts

How often did people attend church at different points in the Medieval Period?

What were important every-village-has-one buildings in the Medieval ages?