[5th_bike]

The starter looks like a metal cylinder on its side at the front of the engine, it has one cable that connects at the top at the right side, under a black rubber cap. This (black) cable comes from the starter relay (AKA starter solenoid) in your first picture. It is the "other" thick cable, about as thick as the red cable from the battery. Please refer to my previous post as to where to measure resistance.

My son is a UMD student who lives in College Park as well and I'd go there and try help you but I never dealt with carb issues (what I think this is because it turns over and doesn't start) before so I won't be much of a help.
if you don't feel comfortable cleaning the carb yourself you could try a shop. Or maybe there is a "Terp riders" organization where you could get help.

For cleaning the chain, use kerosene. For lubing it, use motor oil. Sparingly. I use a paintbrush to clean it, over a paint tray (to protect the garage floor), paper towels to dry the kerosene off, and a paintbrush to spread some motor oil to lube it.
Don't worry about that little bit of rust on your sprocket. It will wear off with use. Remove the cover and brush some oil on it.