2) You can either sign up for a hospital (Aleman, Italiano, etc) or go with one of the private plans. Hospital plans are cheaper but you are tied to that hospital. For private plans, OSDE is probably the best but most expensive. Swiss Medical is another well known plan. Medicus has a very inexpensive plan if you sign up for the expat discount. You can sign up for any of them on a tourist visa. I assume you do realize that in the event of a serious medical emergency, you can be treated at a public hospital for free?
2a) No idea on your possesions - I think you would need to keep your travel insurance for that. I would evaluate if it's worth it or would be cheaper just to replace the things if something happens.