Lets see options one by one :
I) The language here will be regular as intersection of regular languages will lead to regular language only..And we know that given a regular language , whether it is finite or not is a decidable problem..This can be seen by observing the DFA..If DFA contains a state which contains a loop and that state is reachable from start state and that state is either a final state or leading to final state , then the language will be infinite..
II) The regularity property is undecidable for context free languages..Hence it is undecidable..Details regarding this : https://cs.stackexchange.com/questions/19482/why-is-deciding-regularity-of-a-context-free-language-undecidable
III) Now equivalence of two CFLs is also undecidable property..Hence given 2 PDAs which is nothing but characterising CFLs , whether the 2 CFLs will be same or not cannot be decided..
IV) Given a grammar , it is context free iff its productions are of the type V --> ( V U Σ )* .....Hence it is a decidable property..
Hence B) should be correct answer..