Yes, the plug I'd used to drain water that gets in the boat either from using it or from a leaking tarp etc. If the plug is in and there is a leak in the cover, it will fill with water and do allot of damage, with it out it can't get filled. MAKE SURE TO REINSTALL BEFORE PUTTING IT IN THE WATER.
The serial number is generally ground on the port side of the upper drive section. If it can't be found the a year or motor information could help when other more knowledgeable experts chime in.
As for the leaking oil, can you take a pic of where it is leaking from. I suspect you mean the shift shaft in the front. A pic of the entire drive could help determine what kind of drive it is also.