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Use hand wraps and get your instructor to do it for you as it’s somewhat complicated to do properly and for the first time. Then ask for some thick gloves and work your way down. Or you can just keep punching with wraps only, don’t screw up your knuckles real bad and your hand conditioning should be excellent in a month or two.

Yes. Keep it clean. Those gloves get wet and then sit, they are infected with bacteria. Keep the cut covered and clean.

Is it from the ring, as if in between the fingers, or is it between the knuckles? In between the knuckles means your fist is not lined up correctly. You should line up the ulna and radius in a straight line with the 1st two knuckles. ONLY the first two knuckles should be making initial contact with the bag. The other knuckles should only be making "secondary" contact after the first two penetrate, and the punch follows through into the bag. You may also be "sliding"m the punch as you hit. Make sure your fist penetrates straight in to the bag, then pull it straight out.

most people (even mma fighters) use boxing gloves on the heavy bag…maybe you should invest in those

Don’t use MMA gloves on a heavy bag. Use bag gloves or boxing gloves. Shoot boxing gloves are another option.

Are you wrapping your hands too? If not that could be one of the reasons. Also if your pinky and ring finger start bleeding you may be punching with the wrong knuckles. You need to use the index and middle knuckle. The other guys are right as well, you should be using boxing gloves, bag gloves and I think some places make MMA bag glove but I am not sure.

suggestions.
ask coach
wrap hands
use proper gloves

To hit the heavy bag, you are supposed to wrap your hands, and use at least 10 oz gloves.

That’s what you are doing wrong.