1. You should answer questions truthfully, but unless asked (including on written documents) you can be circumspect about sharing negative information.

2. See #1. That would be an untruthful statement. If you correct it, though, you can expect the petition to be denied. Time for an immigration lawyer.

3. I'm sure somebody has.

4. What do you mean "visa" - didn't you say she's going for LPR status?