abibret

Like @LoopyLex said, you can't be a TA while on a co-op term, although you'll make more as a co-op student than a TA. However, the TAship doesn't just disappear - it gets deferred. For me, my fall TAship (when I did a co-op) was deferred until next fall. I'll lose the funding because I'm graduating in the spring, but if you were going to take longer than the two years to graduate, then you could just do the TAship in a later term.

Just email them and say that you are waiting to hear from NPSIA, and ask if it would be possible to receive an extension on the deadline.
This can sometimes also serve as a good negotiation strategy. If they know you have interest in another school/program, and if they really want you to accept their offer, they may increase their funding offer as an incentive. This happened to me - I asked a different school for an extension on the deadline because I hadn't heard from NPSIA, which they provided, and a few hours later I received another scholarship offer from them. 

Hey Sagnik - I'm a current second year student. This is totally normal. I went straight from undergrad to NPSIA. We also found out late March about admission, and I received an email on April 1st explaining where to send the transcripts. I think your transcript just needs to get there before course registration in June - you'll have a conditional offer of acceptance until they receive your transcript. You won't be able to register for courses until that happens. They received my transcript in June. Your undergrad institution has to send it.

I am a current NPSIA student heading into my final semester in January. If anybody has questions, feel free to send me a private message and I'll do my best to help out. Good luck with your applications!

I am a current NPSIA student heading into my final semester in January. If anybody has questions, feel free to send me a private message and I'll do my best to help out. Good luck with your applications!

Typically about 3 weeks.

It is possible, but not recommended, to complete the program in 1 year.