No, they arresting officers do not have to have the warrant in their possession, only the knowledge that it exists.
Warrants don't "turn into" something different. When a warrant is issued it is either issued for a misdemeanor or a felony offense. It doesn't change.
Unable to figure out what you are asking.
Not necessarily, but because of the huge common border they share, the two nations DO cooperate in locating and/or apprehending fugitives and share their criminal databases.
You don't. Warrants never expire. They exist until canceled by the judge.