Questions about Xiaomi Watch 2 Pro

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.

The watch supports eSIM, but the eSIM function is not compatible with every supplier. For example, in some regions, such as Ireland, the eSIM version is only compatible with Vodafone and O2. It is advisable to check with your mobile phone provider whether they support the eSIM function before purchasing.

Naturally

Yes, myswisscom offers the option of requesting an eSIM for the watch if it is included in the plan. otherwise it can be booked separately.

No, mine is running perfectly. I've been using it for 2 weeks and haven't had a single crash yet. However, I have also deactivated 4G as I don't (yet) need it. Maybe your copy is defective...

According to Xiaomi itself no, Swisscom certainly does not work here.