Serious question: is it kidnapping if US Marshals go into Mexico and grab a fugitive to bring him back to the US? Maybe it is, maybe we (generally, as a country) are okay with it under certain circumstances or for certain offenses.
If it happens as you describe, then it is definitely kidnapping.
It's kidnapping under Mexican law, but I can't think of a US law that would ban it.
Does it happen frequently? (Serious question, I don't know).
I have no idea, I just know it has happened in the past both with and without approval/consent of Mexican officials. I don't think they'd be super public about it either way. Either it happens very rarely and that's a safe way to evade capture, or it happens every day and people will stop running to Mexico.
I don't believe it is the case that US law enforcement agents can go into Mexico and arrest people. Can anyone clarify this?