Welcome to the forum! Many questions, so I try to keep it short:
I may lose access to US-based ETFs
See this thread, especially summary by @wapiti :
Is Switzerland in the EU? No
Does European laws apply to Switzerland? No
Is there a similar law in Switzerand? No, ( at least not yet)
Isn’t putting more than 250k on a single fund too risky
No, funds don’t have an inherent risk themselves that could lead to bankruptcy.
they recommended life insurance/3b pillar
In >98% of cases that is bad advice, @San_Francisco already mentioned valuable points.
maybe starting with a small sum of around 20k
I’d suggest using the cost average effect and go for 15 to 20 kCHF/month to spread your 250 kCHF + new savings over 1 to 1.5 years. Especially as we are close to all-time highs, otherwise you inadvertently are timing the market. Don’t worry about paying some minor fees along the way, ramping-up too fast is a bad idea.
Does this strategy make sense?
Yes, keeping bond/less risky asset allocation is important when planning to buy real estate. For simplicity, look at your portfolio without pillars 2/3 and go for target allocation with that portion. Review asset allocation after buying real estate.
using the 2/3 pillar for a downpayment of a house when leaving Switzerland
Not an expert, but in general if you leave the EU indefinitely (or at least with the intention to not return) you are free to use your pillar 2 as you please. Technically Postfinance is correct in saying you can’t use pillar 2 for a downpayment in the UE, as this does not count as “WEF-Bezug” and is not permitted under that umbrella, but irrelevant as you would dissolve your pillar 2 completely. You also mentioned Spain, in that case the “WEF-Bezug” works in principle as it would in Switzerland.