We say, "I had deja vu", or "a feeling of deja vu". We pilfered an adverb+verb from the French (déjà vu="already seen"), so I guess we're uncomfortable about treating it like a noun. ;) So we never say "a deja vu" nor "the deja vu"... simply "deja vu".

Yes you can.

"I have/had a feeling/ sense of deja vu" would be besser.