Yes, the higher support levels have international options, although the details depend on where you are. (although afaik the apple-like case of "bring to service partner, have them handle it" is covered very widely, but .e.g you won't get on-site support everywhere. But well, with Apple you can't even get that in your home area, so yeah...)
Yes. I have had next-day on-site support for Thinkpads in Europa, South Africa and the US. For devices not necessarily purchased in that country. The only question I got was with a German Thinkpad in the US when the power brick failed: "Do you want the replacement with the European plug or the US plug?". Everything else was fixed promptly without any questions or issues with warranty status. And no Thinkpads don't fail that often, I just have used them for more than 20 years.
If you pay enough (I only checked commercial ProSupport Plus[2]) you get service and support anywhere where Dell is selling that product [1], as long as you travel less than 6 Months.
I'm not sure to be honest. I was not aware of that as an option when I bought my previous Dell XPS around 5 years ago. Maybe things have improved now though.
