Changing tires just takes practice ... and some tires can be really hard to stretch over the lip of the rim. I use three levers sometimes, and a metal one is handy, sometimes. Check YouTube for videos, Someone there might have a tip or two i cannot think off.
Yes, you will need to buy a portable pump. I don't spend a lot but for $20-$30 you can get a good one. Make sure the pump will inflate to sufficient pressure for the tires you use.
You can get a handlebar bag to carry the lock.