Immediately file for divorce. Have him legally evicted from your residence. You do not have to get him an apartment that is extortion. Do not worry about him filing VAWA. They know false claims when they see them.
Sister cannot come here and work. Taking care of your mom is considered work. She can apply for a visitors visa but with you and her living there I doubt it will be approved. Also, how do you plan to cover costs of surgery?
You still need to meet the requirements to file.
VAWA only allows to file for citizenship under the 3 year rule based on marriage to a US Citizen, nothing else.
USCIS will not advise you to commit immigration fraud. So that statement makes no sense. Also you cannot adjust on ESTA so they would not advise that either. I don’t believe you got your facts straight.