The two posts above sum it up pretty well. I'm GPR with another TOC, and whilst I don't know what role you are GPR for or what your contracted hours are, this is my experience so far;
Essentially, as stated, the role is to cover Annual Leave and other planned absences. Wherever possible I get a full 35 hour week, although currently I am 'spare' (i.e. no absence or leave to be covered) so I am assisting at one of the two stations that I cover.
My roster is planned on a weekly basis, with the roster out every Thursday so if it's the same where you are they are indeed correct that you will only find out on a weekly basis what your next weeks hours are. I work 5 x 7 hour shifts a week where possible, for a 35 hour week, so I get two days off somewhere in that week. It entirely depends what I am rostered to cover as to what days off I will get - this week I have Sun/Sat, next week is Sun/Wed.
It might be possible to work out where you'll be covering if you have a plan of your colleagues Annual Leave - I, for example, know there are 4 weeks Annual Leave coming up soon so will likely be covering their rosters for those weeks. It's not 100% set in stone but it's quite easy to work out where you'll be needed.
Again I can't comment for your TOC, but as GPR I don't work Sundays unless I am asked and agree to them. It's nice to have one day a week I can plan something around! I think that is the limit of what I can say about my GPR experience - I'm still relatively new to the industry and this position, so I'm sure others may have more to input!