a) INFINITEDFA is decidable
The language accepted by a DFA M with n states is infinite if and only if M accepts a string of length k, where n≤k<2n
This makes the decision problem simple: just try all strings of length at least nn and less than 2n and answer "yes" if M accepts one of them and "no" if there's no string in that range that's accepted.
if a DFA with n states accepts a string of length n, itself is a sufficient condition to tell that a DFA accepts an infinite language, but we are using upper limit of 2n to stop our testing, if DFA accepts finite language we will keep on testing.