Medicaid is save to use and will not make someone a public charge.

Since they need to know what days you have been out of the country, you should bring the whole passport, and not just part of it.

Usually if it is sufficient when you file it is fine. If you want to avoid any issues, you can file a joint I-864 with the application.

Your five years does begin when you finally moved to the U.S. four months after you first entered.

It may still be possible if you can demonstrate that the offense did not show that you are a person who does not have good moral character.

In theory a mere ticket should not affect your immigration. However if you want to avoid any risk of denial you can wait for five years and then...

There may be some legal argument that it is permitted. And there is a substantial risk USCIS will deem it not to be permitted.

Contact the embassy or consulate and ask them to open the form for you, or you can correct it in person at the interview.

Perhaps you qualify for asylum. Or perhaps you could file to extend your tourist visa status.

It depends on how long you stay out of the U.S.