A partial answer is better than none, I suppose.
1. Only seen one reference to crashing so far. According to Per Jorner, walkthrough version 1.2:
Taking items from super loot bags may mess up map data, causing other squares to behave strangely. For instance, as discovered by Wild Bill, if you grab some Throwing knives from the Quartz super loot bag, leaving the inn by the main exit will deposit you on the wrong square outside or even toss you out of Quartz entirely. Wild Bill also recalls other incidents related to this: "Once when leaving Fat Freddy's casino I arrived inside Base Cochise, rather than back in Vegas. Had not picked up the Secpass B key yet, so was hopelessly trapped inside Base Cochise by the autosave, with no way out! Once when entering Freddy's office there were no characters present there... no opportunity to accept or decline the offer or just attack. Game was locked up, restarted and tried again... same results." Meanwhile, Brendan had a spooky turn of events in the same location: "I tried to raise Gamble on a slot machine, then suddenly it turned into a doctor's office and I think it only cost $4 to examine. So I went to the next slot machine, it too worked for a while and then did the same thing. Soon all the slot machines were these stupid doctor's offices." Well, it would be spooky if it happened in real life, anyway. Effects can include pretty much anything from stumbling across freak messages or spawning groups of invisible enemies to becoming utterly stuck or crashing the game. If you want to cheat in absolute safety, don't use your regular files or disk images while taking the items, and back up your game beforehand.
2. I haven't spotted any corrupted stats.
2a. Easiest way to get extra skill points is to increase a skill high enough that its cost to increase wraps around to the negatives. Studying at a library with a skill at rank 8 or higher can be a great source of skill points. Interestingly enough, if you have an everlasting gobstopper of cash, gambling is your best and easiest source of such a skill. There's only one table (Acapulco club, I think?) where the check is high enough to always be a challenge.
3. I have no idea.