Don't worry about anything being damaged by reversing the polarity.
Being the battery is at least 7-8 years old, chances are it is bad.
You can continue to try getting it started by jumping it with 12v, just don't crank on it too long or leave the ignition on.
Start by cracking engine oil and transmission/rear housing plugs and check for water. Let the water drip out, but don't drain the oils yet. Check the oil levels, if any excessively low, top them up. Check the coolant, top it up with 50/50 antifreeze. Pull the plugs, put a little light oil in each cylinder, let it soak while checking other things.
Next, go to the ignition system. Be sure you are getting power to the coil with the ignition on. Next check the points, be sure they are properly set, and making contact. They may need cleaning, oxidized from sitting. Use contact cleaner, brake cleaner, or carb cleaner and a paper business card drawn between the contacts. The coil should produce a good spark each time the points are opened, it needs to jump at least 3/4" at the coil wire to ground.
Take a look in the gas tank. If empty, look at the rust situation. Chances are the tank will have significant rust unless it has been changed. Look for obvious holes.
If there is fuel in the tank, unless it was recently filled, it will need to be drained and replaced with fresh gas.
For now, you are just trying to get it running, so don't get too involved in the tank. Just be careful that it doesn't leak. Eventually it will probably need to be cleaned or replaced.
There is a drain plug in the bottom of the carb. Pull the plug, turn on the gas, catch what comes out in a clean glass. It should have a steady flow, not slow to a drip or stop. If it is not a good flow, there is a restriction, could be in the tank, the separator screen, the float stuck, etc. Process of elimination to get the fuel flowing, and stopping when the bowl is full.
Look at what was caught in the glass. If rusty, dirty, water contaminated, cloudy, the tank is contaminated. You may want to use a temporary fuel tank for test purposes.
Before putting the plugs back in, spin the engine through to blow the excess oil out. Check for spark again, this time at each wire at the plug end. Should get 1/2" spark.
Should be ready to start now. If still no start, run a compression test. Could have stuck valves from sitting. They can usually be freed up with rust penetrant and tapping with a small hammer.
Once you get it running, and it appears to be practical to proceed, get a new battery. You will want to polarize the generator, just to be sure since there is a polarity question.
Now, that it is running, take it out for a drive, put it through all the motions. Make a list of everything that isn't right. That way it can all be fixed at once, no going back taking it apart again!
Let us know!