answer
1. They can refuse to cash your chips. MGM Grand, for 5K chips, has been known to confiscate them and issue you a receipt until the player produces an ID or players card which shows the play where the 5K chip was obtained.
2. Requiring ID for cash-outs greater than 3K is now standard practice in Nevada. New Mexico Native American casinos require ID for almost all cash transactions. AC and CT don't ask for anything right up to the 10K CTR threshold. Biloxi casinos vary greatly by casino. IP requests nothing for $9900, Beau Rivage and Grand Casino is like Vegas. LA has a $2K threshold at many places for ID.
3. IF being 86'd the casino usually desires you to cashout because they can get the best picture of you at the cage. Simply refuse and leave without coloring up. If you color up they will try to give you high denomination chips that are hard for others to cash. Of course you can take the chips with you. When 86'd you should always just leave, preferably looking at the carpet most of the way out.
What to do? If you play rated you can cashout up to 10K and just show your players card. (except New Mexico). If you play unrated you have to cashout less than 3K at a time in Vegas if you don't want to provide ID.
Hope this helps.