Let's say I'm a student doing a MSc at a university and I want to change town, can I transfer my credits (for example 60 credits, which is 1/3 of a MSc) and fees paid up to now to a different university ?

I'm not aware of any cases where this has been done and I doubt it's possible.

I know loads of people, including myself who did credit transfer but I doubt you will get fees back. You could talk to your uni finance dept and ask what happens to fees paid upfront if you withdraw.