First the basic situation. I am non-EU, my registered partner is EU (French). We live/work in Switzerland both with EU-B permits.

The thing that triggers all the following questions is that we are planning to buy a house in Switzerland. We even have already visited some houses and have a basic idea where and which we want to buy.

Here goes the questions.
1. About mortgage loan. Is the loan to buy house open for foreigners? What are the conditions (criterion) based on which the bank makes the decision?
2. My parents, who are non-EU and living in non-EU, have some spare money, and they are willing to support us to buy this house. Clearly with their money we can make a smaller loan. The thing is that we want to do it in this way that they "lend" us money other than "give" us money. So what procedure is needed to get a proof that we borrowed money from my parents and will return it later? Does a personal signed IOU or promissory note have lawful effect, or we have to get it notarized by some officials?

Thank you a lot if someone with similar conditions can share their experience.

There's no fundamental differences for foreigners getting mortgages. I would suggest already going to see an advisor at your bank (and maybe a few others to get other offers), to discuss in general terms how things would work for you. You really don't want to wait until you're making offers to at least have had preliminary discussions.
With respect to loans from your parents, that really is up to you and how you get on with your parents. There's certainly no obligation to have a notarized document or indeed any document at all, but if you feel more comfortable with that you can obviously do so.