This is a variation on this question with amorphous cardinals replaced with dedekind finite sets.

Dedekind finite sets are sets that have no countable subset, and it is well known that this is a weaker assertion than a set not having a countable chain of subsets with respect to the strict inclusion relation. For example as Joel pointed out in a comment, there can be infinite Dedekind finite sets of reals, and one can construct a sequence of slices of such a set. A set like that would also have an uncountable chain of subsets, but I am interested only in well-ordered chains.

I want to know how long such well-ordered chains can be, and I have the same 3 questions as in the last question (we work in $\sf ZF$, and a "chain" means a chain with respect to the strict inclusion relation):

Given an ordinal $\alpha$, is it consistent that there exists a chain of infinite Dedekind finite sets of length $\alpha$?

Is it consistent that for every ordinal $\alpha$ there exists a chain of infinite Dedekind finite sets of length $\alpha$?

Is it consistent that there is a class chain of length $\sf Ord$ of Dedekind finite sets?

Also, if the answer to any of these is no, does it change when we consider Dedekind finite cardinals instead of actual sets (with strict inclusion replaced by strict inequality of cardinals)?