As you get started, climb with someone who's experienced. It's much safer to climb with another person, especially if you're just starting out. It's good you're thinking about possible scenarios. Climbing requires you to be alert for potential problems.
1. If your hitch gets tight, you could stand up in your footloops (if you're using them) to take the load off the hitch, then work on breaking it open and loosen it a little bit.
2.Don't wear loose clothing, tuck in long hair, and be careful not to allow your gloves (if your using them) to get caught in your climbing hitch. otherwise, your climbing line should be okay.
3. Getting twisted around happens frequently as your rope twists, which generally isn't a big deal. However, be careful when descending not to come down to hard or fast. You don't want to get into the uncomfortable situation of sitting down hard on your foot ascender (if you're using one.)
Mainly, take it slow and keep your wits about you. Hanging upside down in a bat hang can be a lot of fun, provided your feet are free. You can raise yourself up by dropping your legs. If you don't feel comfortable about doing some maneuver, like limb walking for instance, then don't do it. Wait until you have someone experienced around who can demystify the process and help you through it.