There’s a lot to unpack here. So 3 different mechanics serviced the vehicle and all 3 got a battery wrong? This is one of the most basic services anyone can complete on a car, second only to maybe changing an air filter. I’m worried about the quality of shops you are taking it to. If the battery terminals were having connection issues, this can certainly cause issues with the battery. If the battery is discharged beyond a certain point, the capacity of the battery will diminish. If it’s been doing this for six months, you probably have a dead cell or two in the battery. The battery is likely under warranty. Tell them you’d like it tested and replaced. You may have to pay labor depending on the shop but changing a battery on that car takes about 2 ½ minutes. Ask them to check the condition of the terminals because of the issues you’ve been having. If the shop wants to charge you for a diagnosis, take it to autozone and have them check the battery, they will do it for free.

By screen, I assume you mean radio? What parts did you use to install it? If you had to run power, where did you run it to? This is likely a blown ignition fuse.

It’s not going to hurt anything the way it is, but if you are changing the brakes soon, it wouldn’t hurt to hit them with a wire brush. If you want to get fancy, you can strip and paint them, but I wouldn’t bother.