Python chains such relational operators naturally (including in and is).
a() == b() == c() is functionally equivalent to a() == b() and b() == c() whenever consecutive calls to b return the same value and have the same aggregate side effects as a single call to b. For instance, there is no difference between the two expressions whenever b is a pure function with no side-effects.
print() always returns None, so all we are doing is comparing Nones here, so the result is always True, but note that in the second case, print(2) is called twice, so we get two 2s in the output, while in the first case, the result is used for both comparisons, so it is only executed once.
Yes, however, when the comparisons are chained the common expression is evaluated once, when using and it's evaluated twice. In both cases the second comparison is not evaluated if the first one is false, example from the docs:
Comparisons can be chained arbitrarily, e.g., x < y <= z is equivalent
to x < y and y <= z, except that y is evaluated only once (but in both
cases z is not evaluated at all when x < y is found to be false).
Yep, at the python's internals the comparison operators returns nor true neither false, they instead return the 'comparison result' object (cannot remember the class name, it was quite in past), and this object provides the _lt_, _gt_, _eq_ etc etc methods and become 'responsible' for the final result (and the 'comparison result' is casting to True or False at end of statement). That's a magic of semantic control python provides to you :)