If you close an account, it will still show up on your credit report. It will say something like "account closed by consumer." So it will still show you've had the history.

On the available credit line of thought...it's also said that having too many open accounts, even if they carry zero balance, can potentially cause issues as you have the potential to charge up lots of stuff, which could lead to payment issues.

I know more about credit cards that you'd ever want to know, but most if my knowledge is on the business side of things. Comes from years of accounting for a national retail chain.