Battery has swolllen, can see the damage on the device

You should receive everything you need to perform the repair in the kit. Other damages to the device could potentially be to the trackpad, case, and -if it's bad enough- the keyboard. I'd really recommend replacing the battery first before you try looking into other damages as just replacing it may be enough. I've seen MacBook batteries so swollen they are literally crackling and moving after being taken out and the device was fine after the replacement. Just be careful!! :)