1. Skills -> Stats -> right hand column, you get 3 stat points to distribute after each level-up.
2. You can buy painkillers from the vending machine in the medical wing (1 cred each iirc.), showers decrease pain a bit, and there are some perks that will automatically lower pain after each turn in combat. Also, apples relieve some pain, you can snag 4 each day for free from the garden.
3. Alex' quest (mines), doing experiments/milking for the doctor (med wing), selling loot to the vending machines, and there are a few hidden caches of drugs/items in off-limits areas that you can get to. After a while, I find that money becomes a non-issue as I'm looting more drugs than I can possibly use and there isn't really all that much else to spend it on once you have the clothing stuff etc.
4. Special moves can be acquired through perks. Weapons can be looted from some encounters (some inmates may drop shivs, guards can drop stun batons, not sure if drop rates are really low or if the drops only occur on scripted encounters/after a certain level).
As for species, horses are already a thing during character creation. You can roll a fox by selecting canine, then choosing a fox head + tail. You can also make hybrids if you want to mix it up. Lastly, there are mods - enable mods in options and restart the game, then have a look - there's rat, badger, bunny... probably more.