Dutch,
Your termonology is throwing me a little bit.
First,
RG6 doesn't mind being close to a Mast, but, I think i'd use some things called Tie-Wraps. Plastic Cinches that can be put around the mast and wire. Tape has been pretty unreliable, from my experience. And, don't pull it down TOO tight, most Coax doesn't like to be squeezed.
Second:
Satellite and a FM Antenna are probably not going to do well on the same line. You can run a Coax to your FM antenna, and just reverse Balun it, when it gets to your Entertainment Area, if your Amp has the 300 ohm connectors on it.
Third:
Could you mean a Satellite "Dish", I don't know of a Satellite TV Antenna, and if you mean a VHF/UHF Antenna, lots of them have FM capabilities, you can find several by visiting the home page here.
Get back to me if I've misunderstood something, and I'll try to help you a bit more.
Have a good Day
S.W.