Nurse managers do read up on people they select for an interview. Unless you lied, they know you haven't taken NCLEX. You can still be hired (which is awesome). I would just mention again that you haven't graduated or taken It yet.
If they are hiring new grads, they will know that you haven't graduated yet in April. If they want you, they will wait. I interviewed and accepted my job in March when I was a new grad and didn't start until September. My new job, they waited a month for me because I had to give 4 weeks notice at my old job.
Depends on how immediate the need is. Some places will be able to wait, others won't. Just be upfront with them about your availability. Like someone else said, they do look at your application and should see that you haven't graduated or passed NCLEX yet. Interviewers should also be upfront with you about their needs and how quickly they need to get that position filled.