Well, it's a brand new phone and you want everything to be working the a great manner.Neither of these are really problems, it's quite possible to use the battery quicker than the phone is able to charge itself, and dropping 1% off unplugging is not something to be concerned about.
Almost certainly a computer. Most people charge with computers that do not provide enough amperage like a wall charger will. Try charging it with a beefed up iPad wall charger vs. a USB 1.0 port. The iPad will probably charge your phone from toast to 100% in an hour, hour and a half.Are you plugged in via USB to a computer or are you using the wall charger?
You can't overcharge your battery.This happened on my iPad also. I think it's the same thing as the MacBook Pro: it never fully charges to 100% when the battery is at 95% capacity.
Say you have a MacBook Pro that is at 100% charge and plugged into the charger. You remove the charger and the MacBook Pro is then running on battery. You let the battery drain to 96% and plug it back in and you see that the battery won't charge.
I think Apple is adopting this feature in their iPhones now.
This is poorly explained. I'm sure someone can explain it a lot clearer.