I know that for every three months of unemployment, I am entitled to one week's leave. Is that paid? Do I still have to apply to the same number of jobs in the month in which I took the holiday?
I think you misunderstood the question, it's not about extra cash.
When you take a week 'holiday' you don't have to be applying, or available for work, but you still get the same amount of money for the period you're away as you would normally.
No, you're paid for the whole 4 weeks as long as you've given sufficient notice and complied with everything else that month.
If you are entitled to the 1 week holiday in a given month you get paid in full for that month. If you take a holiday without being entitled (you declare in the form at the end of the month if you used any holidays) they will not pay you for the days you have been on holiday.
Each month you receive the slip for the current month which also include the admin section of how many pay days you are still entitled and how many holidays allowance you have.
It depends on the amount of jobs you have to apply for each month, it is not fixed at 12, but basically yes it would reduce the amount of positions that you are expected to apply for that month. More importantly during the holiday week you do not need to be available for an appointment at RAV or interview etc with a days notice so you can travel outside of Switzerland.
It's a little more than that. It's also five days you do not have to be available for any interviews or meetings. In theory, the RAV can call you with 24 hours notice for a job interview and "I'm abroad" is not an acceptable reason for not being able to make it. How likely this can happen depends on how proactive your RAV consultant is and your line of work, but if they did give you a call and got a UK ringing tone, you would likely get in trouble.
The only other thing I remember about holidays with the RAV, that has not already been mentioned, is unlike in real employment, you can't take one two or seven days off, but have to take them in blocks of five - hence the one week every three months, as it is the statuary 20 days per year (if you're over 50, it might be worth while to find out if the increase them, although I doubt it). Oh, and I don't think you can take them in advance.