Trackpad not working, keyboard erratic

Before you order anything the first thing you should do is inspect the battery cells visually.

A quick inspection will make it easier to determine whether it’s an obvious issue such as the battery cells swelling.

Here’s a guide on how to lift the bottom cover:

MacBook Pro 13" Retina Display Mitte 2014 unteres Gehäuse austauschen

Can you confirm this is the correct MacBook model? Input your serial number on the EveryMac look up in here to confirm:

https://everymac.com/ultimate-mac-lookup...

If you do plan on doing a battery replacement, test the keyboard and trackpad before you install the battery (with the adhesive).

MacBook Pro 13" Retina Display Mitte 2014 Akku austauschen

The trackpad cable (which actually runs under the battery under a metal plate) is separate from the keyboard cable. I would suspect that there may be liquid damage inside the MacBook if they are both having issues, you’ll have to open it up and check the Liquid Damage Indicators which are little circle stickers that are initially white and turn red when they are in contact with high humidity or liquid.

Edit: After doing some reading online about this issue, if this is a Late 2015 model it may be actually the trackpad cable being at fault if it’s the cable that runs over the battery and not under the battery.