1. Technically, you should be able to take 10 on the check, as you're probably not going to be casting the spell in a stressful situation. That's most definitely not the intention, but there's nothing preventing it.
Alternatively, a dedicated Wizard will probably have Int 30-34 at level 20. If the DM agrees, you could do something like adapt the Circlet of Persuasion for Int checks instead of Cha checks and get to a high enough modifier, but you probably shouldn't rely on that if you're going to be cheesing CoP.
2. None that I know of. A Wish spell could try to fix it, I guess?
3. You can cheese the system by asking questions about questions to reduce the probability of any one question being wrong (e.g. "Was the answer to question 1 false?" "Was the answer to my question about question 1 false?", and so on). You'll never get it to exactly zero, but you can get close. That aside, the Divine Oracle PrC allows you to roll twice on percentages for divination spells and take the better, which reduces the chance to get a false answer again (from 10% to 1%, if you're at 90% likelihood of a correct answer).
