TFSA and mutual funds and nonresidency

I am a Canadian citizen, studying in the US (on a J-1 status). Right now I am considered a Canadian resident (for tax purposes). I assume that I am still therefore allowed to buy mutual funds with my bank, put money into TFSAs, etc. Correct?
If I eventually give up my Canadian residency, I know that I cannot put money into my TFSAs. Would I still be allowed to buy TFSA stocks/mutual funds with money already in my TFSA accounts? to buy stocks/bonds/mutual funds outside of TFSA?
Thank you very much for any help you can give!

you've already asked Q's on serbinski site. keep the tax discussion there.

You should close TFSA when you move to US. You can always replenish when you go back.

Okay, sorry. I will re-post the question there.
But when I do, could you explain a bit more. Why should I close my TFSAs?
Also, what is the answer to the question of what things I can do with investments (TFSA, mutual funds, stocks) while overseas (buying, selling, transferring from one account of mine to another of mine, buying mutual funds with money already inside TFSA).
Thank you greatly in advance for your help!

are you ahving trouble understanding?