Well, that depends upon whether the police catch you.
A warrant means the police intend to arrest you. So if your id is run by the police when you exit or enter the country, you the warrant will show up and you will be arrested.
If you fly by airplane, your id will likely get you arrested. If you go by car you will likely get into Mexico OK, but could get tagged on the way back in.
Of course, you can cross the border like the illegals do, and then it doesnt matter unless you get caught.
Short answer - get the warrant cleared.
No.
No
In New Mexico, the occupant of a house being searched should be shown the original warrant.
yes you can
If the subject being detained is the object of an interstate extraditable warrant, they will travel to whatever state the detainee is incarcerated in.
Turn yourself in. If the warrant is not still outstanding, walk away.
With a warrant or if he witnesses crime.
Yes
It is a distinct possibilty that the warrant will appear on watchlists while traveling by cruise ship.
Travel in-between states shouldn't get you in any trouble unless some state trooper decides to run your out-of-state plate, license, and finds your warrant. Travel to Canada is probably not going to be possible with a warrant out for your arrest, and even with a DUI conviction you will need to apply for a temporary residence permit.
If the warrant was entered into the interstate law enforcement computer system (NCIC) it does.
Mexico does have an extradtion treaty with the US, however, it is unlikely that Mexico will arrest or detain you, HOWEVER - in the scheme of international relations, who knows WHAT might happen.