You are both legally responsible for yourselves.
If it is in the man's name, then the man is legally obliged to pay it.
"In sickness and in health, for richer or poorer" Legally a husband and wife share all assets and liabilities unless they sign a legal agreement otherwise (such as a Prenup)
No
The husband can sell his 50% of the apartment to the wife or to anyone he wants
Does your husband have to legally and financially support his wife during a separation
No, your husband is responsible for his half. You can pay it for him but he should look for a job.
Not legally. He can only have one wife at a time, anywhere in the world. If he had one in Mexico he couldn't legally marry you.
Vows.
Legally, "widowed". If you have not divorced, he is still legally your husband.
If the deceased person is your wife then I think you are responsible for her medical bills
No. If the other person is legally married to another person in another state, then your marriage is not valid in the USA. You can have be legally married to one person at a time.
In many cases the husband will be held responsible. They are deemed to have benefited from to goods and services.