I am close to Lausanne so I can answer a little. I would live outside of Lausanne, east along the lake. Or the villages around Vevey will get you more for your money, but still with easy transport links.
Schools are so hard to have an opinion on, as they don't compare them. But in general I think that if you stay away from really urban areas the schools are all great. They again, they are less diverse, so it depends on what you want.
Streaming for high school happens at the end of 8P (year 7 in UK). They use an average of the assessments you do throughout the year, plus your score for the end of year exams (like SATS). As a PP says they test French, maths and German as key subjects at this age. German is pretty low level, think like hobbies, days/times, small conversations. The key will be whether DC can learn German from French i.e. know that Gutentag means Bonjour etc as i know that's what my kids found hardest. Maths will be no problem for a kid coming from the UK. Your issue might well be French as they are reading novels, analysing texts, and constantly memorising conjugations. You might want to think about them dropping back a year to give them time to get up to speed on their French. Repeating years is fairly common.
As for sport and music, whilst these are subjects in school, any competitive sport or playing an instrument, is usually done on Wednesday afternoons, when there is no school for all kids.
I've been here 10 years now, and have 3 DDs at local schools, feel free to ask me anything.