Yes Vodaphone does have the monopoly on internet connections in the Pearl. They have a little shop in Tower 12 - near Spinneys - who can sort that out for you.

For TV, I believe TPQ are the sole provider via a fibre/IP system. They have an office in Tower 11 (I think).

In my building they give approximately 800 free-to-air channels at no cost via a Set Top Box they provide. You can upgrade this to various OSN packages by subscription. The IT section then just reprogramme the STB remotely to add the new package(s).
As far as I know - but I may be wrong - the QTel Mosaic system is NOT available on the Pearl. And you are prohibited from installing your own dishes on the balconies. You have to go through the proper channels (pun intended) :-)