Finite / Infinite Languages True/False and why?
False. There are infinitely many finite language. Just think of {0,1}*. This is a infinite set of finitely long strings. or say, it is union of infinite number of finite languages over {0,1} which have strings of finite length.
False. Union of two non regular languages MAY BE regular but it not the case always. This answer explains it well.
False. Lets have a single state NFA having state q0. let 'd' be the transition function. d(q0, a) = q0 and since this is single state NFA, q0 is also final state.
This NFA will accept all strings having only 'a'. i.e. {a,aa,aaa,aaaa...} The cardinality of this set is infinite, hence it can accept infinite languages too.