I believe Sprint's trial period is 14 days (sprint.com/etf). If you're within that time then you should be able to return the phones without any issues.
As far as LTE is concerned, you need to be in an area where Sprint offers LTE. Just because your friend on Verizon has the same phone as you and gets an LTE signal, they're still on Verizon so that would have nothing to do with you getting LTE service on Sprint. I would check Sprint's website (or call them) to see if you're in a Sprint LTE area which I don't think you are.
(I hope my post didn't sound rude as that was not my intention.)
Check out a fun infographic that teaches you how to increase storage, enhance security, improve battery life and clean your device.