Look for a metal tag on the transom. Might have a 217- with some more numbers. Post a picture that helps. The power head tag will have an AV-# that tells what power head was used and what HP. Im gonna send you a private message.
Early ones were made by Mercury I think and McCulloch I think for a year or 2 in late 50's. Whats the model# should start with a W I think. The only year they made a 7.5 was 59 by McCulloch MLM6907A
Parsun marine I think makes them they are a sub par Chinese honda knock off. 4 stroke. If its shutting down when its hot it does that to keep you from overheating it. Is it peeing good water stream?
Looks to be fine to me. Running it in a barrel is about as close as your gonna get to the water. Ear muffs I think are only good for some things, I always try to run in a deep tub or trash can