Assuming he has a 5 in Genjutsu stats, he must be pretty good at it. He also was able to move his hands when Itachi put him in a Genjutsu. But, no he's not immune to it.
If he was at full strength he could utilize sage mode in batle and use his newly found brille to block out light to stop visual based genjustu.As he is now he can probably dispel most genjustu except the ones of itachis class obviously.He is not easily caught in a genjustu as most are
He has immense knowledge on Genjutsu and can presumably perform countless Genjutsu, but no, he is not immune to it. Although he can resist it better than others.
He's not immune but like has been said before he has better resistance than most. He was able to move during Itachi's paralysis genjutsu, and Itachi is probably the strongest Genjutsu user in the narutoverse. He'd probably be able to break most other genjutsu with ease.
he is pretty good at not getting caught in it but i would actually say it is probably his biggest weakness that is why itachi can beat him so easily and dont try to defent oro and say he would beat itachi even oro said him beating itachi is a foolish dream