1. If your rear hub now is a 7-speed cassette (not freewheel) it'll fit. A new lockring will come with the 11 tooth cassette. You have to use it.

2. How old is your chain? I'm a believer of buying a new chain to go with a new cassette.

3. I wouldn't worry about the 11 tooth cog wearing out too soon. In fact, I doubt you'll ever wear it out because your 16 or 17 will die first. 53/11 is a huge gear so you'll need stronger legs to turn it.