No, unfortunately esim doesn't work with Galaxus Mobile, only Salt and Swisscom and co. with Xiaomi smartwatches. It's actually a tragedy, I was lured with one year free esim for my watch and switched to Galaxus Mobile, I regret it to this day.

I don't know, the battery life of this watch is already catastrophic (less than 2 days with just wifi), I'd read that with a Sim card it's maximum one day. I'm looking at another watch with a battery life of at least 1 week.