yes
Anytime you need.
Yes, you need a passport to go from the U.S. to Mexico because Mexico is not part of the U.S. If you were going to a U.S. territory and you were a U.S. citizen, you would not need a passport.
That's going to depend on how you get there and where you start from.
This makes no sense, but I think you mean if with an expired passport you can travel from Mexico to New Mexico or vice versa. In that case no, you need an ID or birth certificate if you are going to Mexico; if you are going to the US state of New Mexico from Mexico you need a passport AND a visa issued by the US government.
A passport if flying there or a driver's license if going by land.
To travel to Mexico, you will need a valid passport. Additionally, depending on your nationality, you may also need a tourist visa. It is recommended to check the specific entry requirements for Mexico based on your citizenship before traveling.
You need to wait for at least one year before you remarry.
At least three months before the expiry date
No. Last year the law was changed, you need to have your passport with you when going to or returning from Mexico.
People bitten by healthy, immunized animals are unlikely to need post-exposure prophylaxis (PEP).
If you are going to Mexico and have a passport you do not need a driver's license if you are flying in an airplane. No. Actually, if you are not driving but simply crossing the border with a passport, you should not have problems reentering the United States from Mexico.
To fly into Mexico, you typically need a valid passport and may also require a tourist visa, depending on your nationality. It is important to check the specific entry requirements for Mexico before your trip.