One thing you can try is to carefully remove the shift key from the keyboard. You will see one or two clips and possibly a metal clip or something. I suggest taking a picture before you remove any clips. Then check to see if the rubber underneath is intact and cleared from debris. I recommend powering off the CB and use a Q-tip with rubbing alcohol to clean the area. It could be sticky or something is preventing the button from pressing down. For a Dell CB, I had to put a piece of folded paper because a student removed the rubber underneath the key. I would see if it exists and if that's not the case, see if the rubber can be moved. If so, carefully move it and see if you can press the button underneath and see if that works.

That is very possible. If you have a multimeter, test the battery if you can for charge. I would return battery since it's not the phone causing the problem. Also, is the battery the same type as the old; voltage wise.

It's possible the throttle body needs cleaning or check the hose around it. You can get a cleaner from most auto body shops. The one I go to is AutoZone down the street from me. It's also possible your spark plugs may need a changing. It's a pretty simple DIY job. When was the last tune up. Try changing the fuel filter as well. Change air filter too. Good luck.