Never mind, we all get confused in the beginning. We'll try keep trying anyway. :)

You are right sorry, I confused the verb 있다 with 이다. My bad :|

If there is a subject, we should add 이 or 가, and because 있어요 exam here is treated as subject, I think because I'm also in level 1. But you know, I took examples in class like: 어니가 있어요? So we've added the particle here.

I might be entirely wrong (I'm not a native and I'm just barely a beginner in korean) so please consider that, but shouldn't 시험이 be without the "이" and be attached to 있어요? (without the space in the middle)

Could "행운을 빌어" mean wish me luck?