I assume by “sailing visa” you mean C/D visa. He can’t use that for the purpose of tourism. With the denied ESTA, his only option is to apply for a B2 visa.
You will want to make sure you give them absolutely EVERYTHING. Even if the actual crimes/arrests/infractions are not enough to impact the case, failing to provide documentation could cause a denial. We have seen that happen here on VJ.
We did a K-1. No one (from the county marriage license office staff to the wedding officiant) asked to see any documentation related to immigration status. My husband used his unexpired NZ passport as picture ID until he was able to get a Washington state drivers license.
You can marry anywhere, but the CR-1 visa is definitely the way to go. It will take up to two years.
Unfortunately, since entering the US on a tourist visa with the intent to stay and adjust status is immigration fraud, separation is an inevitable part of the process for almost everyone.
Hopefully you have good insurance for your mom, and a surgeon willing to do that surgery on an 80 year old.
Your sister can apply, but the “emergency” situations for tourist visas are for life and death situations for someone in the US, and your mom is not in the US.
What you’ve made “up to this point” is past income. You need to calculate your current income and provide supporting documentation in the form of W2s. If your income is marginal, I’d recommend having a joint sponsor lined up.
But, you always say they can’t deny entry to LPRs?
Also- with no exit controls, how do they know when an LPR leaves the country for say, 9 years, like that one case? Just passenger manifest info?