As I mention above, the way I did this was to buy a low-cost/locked/unactivated iPhone 6s and paired the watch to it. It thus provides in-home monitoring of such events; I can confirm that it works well since it got inadvertently activated a couple of times (the first watchOS version with this feature seemed to be prone to false positives) and I had to talk to the emergency agent on her behalf to state that everything was ok for now.
Can I have one iPhone (in USA) and two watches - one in USA (me), another in Europe with my dad attached to local European SIM card to call local European number if he falls?
I don't think so unfortunately - the cellular watches are weird in that they must be on the same cellular network as the associated iphone. The recipe I suggested above works with the non-cellular version of the watch and counts on being on the same wireless network as the phone. So imo, you will need one iphone per watch. However, I have been able to get refurbished iphone 6s devices for as little as $60; you probably don't want anything older than 6s as it is the oldest device that can still run iOS 13 and thus future proof for just a little bit.
You are right - that should work well as well I believe due to its 6s internals. It's a good idea too: in the US the SE can be found even cheaper than the 6s.
