(1). "it sucks" - is it a vulgar expression? It certainly is not elegant.
Can I use it on a formal occassion? I wouldn't.
(2). "sucker" - someone who is easily duped. Again, is it a vulgar expression? It's fairly informal.
Can I use it on formal occasions? Not really., though I doubt if it would shock anyone.
If by 'vulgar' you mean 'rude, impolite', the word sounds dated to me.