IMHO cutting just the cap of a stringer and digging it out then fitting a new one in would be tedious and time consuming, not to mention the bond may be questionable. I would consider taking all but an inch out so you have a bit of a guide.
You need a motor, get one, what ever it is the folks here know how to install it. You get a motor and help is available. Lots of opinions and most are good.
Yep, some times folks have fun but not necessarily is it help, although most of the time the information given will be useful but maybe not for the present question.
I had a 1979 Scorpion 210 and now have a Searay 220 . Both have 5.7 engines but the Searay is 1000 lbs heavier. The scorpion was agile and quick, the Searay is a slug in comparison but it's a damn comfortable ride and still has a good top end.
You have a 50hp engine on a 20 foot boat. If you have been happy with the performance I would stay with the OEM prop. I suspect the prop you have is all around and best for your needs.
I was employed by hunter marine back in the day and deck leaks from rain was always a problem.
Your problem is different but the same idea will work. I had to seal the known deck leaks and cabin then look for leaks with soapy water.
You need to get some manuals for the engine and drive you have and do not activate anything until you have at least a glimmer of what it is or you can damage it further.