Been having electrical/FOB problems with my Dart on and off for a few months. Both sets of keys do this

First, the doors would randomly unlock/lock just by going near the car and/or placing your finger/thumb on the button without even pressing it. Other times I'd be sitting in the drivers seat and before I could even place the keys in the ignition the locks would activate. Same thing would happen with the trunk. One time it took me 5 minutes to close the trunk because it kept opening after I closed it without me even hitting the button. I would be sitting in my house and the trunk would randomly open, same with the doors locking/unlocking also.

I figured it may be the FOB battery, since I had yet to change it since I got the car. So I changed it in both. That seemed to work for a couple weeks, but now the unlock button doesn't work at all on either FOB. The other day I ended up having to manually unlock the door, which of course set off the alarm. Luckily it shut off after about 10 minutes. The lock and trunk release work sometimes, and the remote start works, but there's about a 10 second delay with it activating.

Is this a major electrical issue? A loose wire? A fuse?

For now, I've just been manually locking/unlocking my door. But, I'm afraid of the doors randomly locking and being stuck in the same situation I was with the alarm going off for 10 minutes. If I take the battery out of the FOB will I still be able to start the car?