I'm not familiar with universities outside the ETH rules (ETHZ/EPFL only) but students are paid a salary at these universities and hold dual status as employees and students. I'm not sure if their tuition is waived. Even if they pay the same tuition as masters or bachelors students this is usually around 800-900 CHF per semester, the cost of 2-3 months health insurance. Not money you want to pay if you don't have to, but it isn't UK or US fees.
However there are definitely time limits. You would find it hard to be enrolled on a doctoral programme for 6 years or more especially if you aren't about to imminently graduate, and this is likely the main motivation behind the advice given the proposed 3 year break in China.
Only PhDs are paid. I think the salary scale starts at around 51,000 CHF. That's a lot for other countries but it isn't for Switzerland. The exact amount is public knowledge and you can find it if you look. It is slightly higher for ETHZ, but not much.