To my understanding, the soldering is losing connection and when you heat it up you make it more malleable. If your're not good with a soldering iron then you need to take it to someone who can re-solder the sim card port back on.
I would try getting another screen and seeing if that one works. Not sure why you would be getting constant vibrate. Depending on where you bought the screen replacement, there are a lot of people out there trying to scam and send crappy products. I have had the problem quite a few times.
The part you are looking for is under the engine cover. Should be 4 or 5 bolts to take the cover off. The part should have a wire or two coming out of it. It's small and one side of it looks like it has been filled with hot glue. That part takes the spark from the electromagnet and feeds a charge to the battery. The part should be held on the side of the engine with one bolt.
There are two things to keep the blades from turning when you don't want them to. There are brakes on each spindle the is holding a blade and when you turn the blades on you are moving a pulley to tighten the belt that spins the blades. Take the covers off the spindles on each side of the deck and check that the brakes are engaging and that the deck belt is getting loose enough when the blades are not engaged.