- what kind of posts do you have in medical engineering: repair, asset management, quality, project manager...(my experience is more about management than repair)?
It varies from hospital to hospital everything from a basic repair service to full equipment management.
- do you know if my french diploma can be recognized in a UK hospital?
There is no formal UK registration or requirement (at the moment) so people are employed on experience andd general qualifications. It would be a good idea to find out what UK qualification is equivalent to yours.
- does every private/public hospital has a biomedical department?
No it is not in every hospital but most do.
- do you think it's realistic for a french biomedical engineer to look for a job in a british hospital (after some english courses!)?
Yes Your typed English seems fine to me.
Robert