First the disclaimer: I'm not an electrician.
Yes, on the APC you can use the 30A along with the 20A receptacles on the UPS. The obvious result will be the battery will drain quicker as it will have a larger load.
Yes, with the proper adapter you should be able to connect the 20A plug into the 30A receptacle. The seem to be readily available. It should not hurt anything as you will be drawing less than what the outlet can provide. Always a good thing.
The only thing not optimal here is that the UPS could supply more than the rated 20A if something where to go wrong. However, I'm not sure what that would be, and I would assume the power supplies have their own protection circuitry.
Hope this helps