That person is allowed to remain in the U.S. until there is a final decision on the application. The government has 90 days from filing to give him employment authorization--assuming you correctly applied for it at the same time you filed the I-130 and I-485. The Seattle district is fast on these cases. The person should have the interview 3-4 months after filing. In the meantime, that person is an adjustment applicant. No actual status, but allowed to be here.
She should be Ok, but be aware that iIf the government has reason to believe the marriage wasn't bona fide, and the case comes to their attention, they can initiate proceedings to rescind the green card even after the condition is removed. She should be careful to retain evidence the marriage was bona fide and what was going on that led to divorce just in case it comes up
I recommend you contact an attorney. The government does get suspicious when a U.S. citizen petitions for various foreign spouses, especially when not much time has passed in between. Apart from the potential proceedings to rescind your prior spouse's permanent residence, you could potentially be facing criminal charges of fraud, if you can't document the facts of the abuse. I highly recommend talking with an experienced attorney before doing anything, including before getting married again.
I urge you to get an attorney to assist. you. You seem to have done a great job so far, but it would be easier to get a lawyer. I don't believe any attorney would try to tell someone in a couple sentences how to do a whole case, not to mention without ever having reviewed the entire history that has already happened. You aren't done yet.
It happens fairly frequently that folks give the money to a US citizen or LPR or someone available to go there to post the bond. Unfortunately, it may not be possible for anyone other than that person to get it back. You'll need to track him or her down.
It shouldn't. For immigration purposes the issues are whether you have a communicable disease that may affect the larger society (which is why they test for TB, etc.), if you have a medical condition that may may cause you to fall into distress, and be unable to care for yourself, if you have sufficient resources for medical care, etc. (affidavit of support will be looked at). If you have a drug problem or mental defect, again, that could have an impact on the community or make you unable to...
You should file the I-751 with lots of evidence both that it was a bona fide marriage and also what happened that it ended in divorce. You will likely receive an interview. You should get a lawyer on this one. You need to discuss confidentially the history of the marriage, how/when you met the new person, why the marriage ended. Marrying someone else could be problematic for showing the prior good faith marriage. It all depends on the facts. Seriously, get a lawyer. This forum cannot...