Yes, 1 conductor is live, the other neutral (just like a normal plug)
Yes no problem the transformer should run a little cooler as well.
Depends. Some smaller stuff can usually run on both, in which case it will be printed on them. If it isn't, you can't run a 220v item on 110v.
45
12-2 can easily support a 220V 1.5 HP pump out to 200Ft. However you may need a separate #8 ground wire in some states.
Your black wires are your hot wires. The white is your neutral or common. It would be best to run an equipment ground (green wire) too.
No
No. Attempting to run an appliance on insufficient voltage can cause damage to the appliance and can be dangerous. Call an electrician and get him to install a 220v plug
Short answer: No. (unless you like ruining motors) Longer answer: Not really, but there are some motors that can be re-wired so that instead of 440v they will run on 220v. However, this is not that common. Conclusion: Check the motor to see if it is dual-voltage on it's nameplate. If it is, you can re-connect it to work on 220v. If it is NOT a dual-voltage motor, you will absolutely ruin it if you connect it to 220v.
yes <<>> No, the ground wire is never to be used as a neutral. In this case if you need a 120 volt circuit from the 220 volt circuit a three wire cable (3C #14) must be installed.
n you run thhn wire in a cable tray
No, the compressor& fan will run too fast and will more than likely be damaged. It may not be damaged but I would not take a chance.
To make a patch cord for this setup, you will need a 4-prong 220V plug that matches the generator's outlet, a length of appropriate wire rated for 30 amps, properly sized for the distance between the generator and compressor, and a 3-prong 220V plug that matches the compressor's inlet. Connect the wires according to color-coded standards (red and black to the hot terminals, white to the neutral terminal, green to the ground terminal). Make sure the wire gauge matches the amperage rating to avoid overheating.