1) do the Swiss doctors speak English? can you navigate the system with basic/intermediate French?
Yes many do, once you're here its easy to ask around for a referral or whatever. You have choice here. For example many / most doctors have their own radiology depts or one close by, ditto blood test places, so they can cover most stuff without sending you to hospital (as the UK would do). In Switzerland generally if you need treatment you get it, there and then, unless its a major operation.
2) - are there any towns around Geneva which are known to be particularly family-friendly, for people who choose to live outside the city?
Yep many, but initially as a first timer you might have to live in the Canton that issues your permit, so for example, if Geneva issue you a permit for work, then your'e bound to Geneva.. equally so for Vaud and so on.
In Canton Geneva it depends also where you work, because commuting around the lake from say Hermance to the UN can be longer than you might want (not relative to London of course, but in Swiss terms a 30 plus minute commute is quite long). Outlaying villages such as Satigny and Russin are family friendly, as well as big wine producing areas, and some districts within Geneva are lovey too, such as Eaux Vives, or Petit Sacconnex or even Chambesy.
In Vaud, all down the lake coast there are villages that are lovley, from Coppet to Founex, to Nyon, to Prangins to Gland, and even Lausanne.
When you know where you will work its best then to ask for reccomendations and ideas.
3) what are the specificities of the real estate market for foreigners who want to rent or buy property? I understand different rules apply for foreigners as compared to locals, but I might be wrong.
Renting here is very competative, especially at decent price levels. So you need to be quick or need help from a relocator agent. You're limited generally to 3 times your salary as max rent... agents are arrogant here and dont have to work for their money, although recently its gotten a little better.
To rent a place you need a residents permit, proof of earnings (contract of employment), and certificate showing youre debt free... plus between one and three months deposit... etc yada yada usual stuff.
For a two bed apartment you're looking at CHF2500 - 4000 per month depending on location.
For a 3/4 bed house (semi detatched) CHF 4000 per month upwards.
To buy, you need a B permit as EEA EU passport holder, or a C permit (after 5 or 10 yrs depending on nationality), plus the 30% deposit... its best to wait till you're here, and not rush this one, since you'll want to find an area you like first, then the house etc.
Unless youre already very wealthy, nothing here will happen for you without a job. get that first then decide about where you want to live, how big a commute etc.