Hi Dmeyer07,
Congratulations on your first post on the Forums!!! :)
1.) YES, your 50A shore power plug should have four conductors at each end. Two hots (L1 & L2), a neutral and a ground. Any properly wired campground you go to with 50A service will have a 50A receptacle for a 4 prong plug. Personally, I would CORRECT this issue IMMEDIATELY. This could be a safety issue and depending upon how it's wired, you might be jeopardizing the electrical appliances in your motorhome. (See additional comments below about it being wired for 30A service only.)
2.) 50A service is 120V/240V service. The vast majority of RV's internally use the connection as two 120V, 50A lines sharing a neutral. There will be 240V across L1 and L2 (L1 and L2 are 180 degrees out of phase with each other), but there will only be 120V between either L1 or L2 and Neutral. Your generator is also 120V. It puts out two 120V hot lines, but they are in-phase with each other, so you won't see 240VAC across the generator hot lines. You'll see approximately 0V across the two generator hot lines. Most likely nothing in your RV uses 240V. However, some newer, mostly high-end rigs, DO have 240V appliances with 240V generators as well.
3.) I'll let someone with more experience with inverters answer this question. :)
50A RV service is the exact same service you will see on a modern 50A electric range or electric dryer outlet in a house. Same NEMA receptacles and plugs.
Thinking more about your 3 conductor plug...I think it's likely the previous owner decided to only use a 30A connection to the rig so he wouldn't have to handle the extra heft of a 50A shore power cord. Can you post a picture of the plug? The 50A cord uses much heavier gauge wire and the cables are definitely much heavier, bulkier and harder to wind up, especially in cold weather. The previous owner might never have needed anything other than 30A, so they just used a 30A cord. (30A service is one hot, one neutral and a ground.) If this is the case, you'll be OK to use it. It's not a safety hazard or a hazard to the appliances on the rig. BUT you'll only have 30A of electricity available.
You probably know this, but just to be complete. A 30A service can provide up to 3,600 Watts of power to your RV (120V * 30A =3,600W). A 50A service can provide up to 12,000 Watts of power to your RV (2*120V*50A=12,000W). So there IS a noticeable difference in available power between the two systems.
Good Luck,
~Rick