Very uncommon from the late Carolingian era onward. One of the more notable ones that survived until around 1500 is that of Ditmarshen at the border of Denmark and the HRE.

Degrees of peasant obligation varied even within the manor or village: while in theory everyone was subject to someone else up to the king, in practice a significant rural minority were free of most or at least some of the more oppressive burdens of villein status, though still subject to universal charges,

Crucial to the system (though much abused) was the role of "custom": a lord couldn't just change the arrangements without a legal cover, and the evolution of estates through successive periods of greater or lesser unfreedom meant that neighbouring holdings might operate under quite different terms, while the need to people newly-reclaimed land with capable tenants might result in milder conditions even as manorialism matured.

Was there a link with market exchange and prosperity? I'd say yes, because when we can identify economic divergence among western regions it's in the areas of least oppression that we later tend to find the economic frontrunners, Holland with its extensive reclamation from the sea being of course the most striking case.

Having more time to attend to your holding and having to surrender less of your produce or limited cash seem likely to have stimulated innovation and commercial engagement. The reverse may paradoxically have applied in a later period when taxes are said to have acted as an incentive to greater effort and output, but at this stage of modest surpluses the development of a commercial sector and freedom to adopt new techniques were probably of greater value.

"Peasant" is a very general term that have very little social meaning. Peasants were people who grew food (including raising animals) and they could include anything from a slave to rich free farmer who could himself own slaves and servants -and anything in between, depending on time period and location.

In popular culture Medieval "peasant" is associated with "serf", but that's completely wrong association.

Medieval European societies were very hierarchical, starting with very strong hierarchy in the family. "Equality" basically did not exist at all anywhere, it could only exist between people of the same social status, that is you could find it in institutions like guilds (and then only to a degree) and not places and communities.