CAP413 is fine for the RT exams, but I never follow it exactly when flying. Keep it clear and simple and nobody will care if you're following the exact CAP413 formula.
In particular, I hate the suggested reply to 'pass your message'. So does everybody else, it seems, as nobody else seems to use it either
I stick with a simple Who you are (G-ABCD, PA-28, from A to B), Where you are (overhead x, alt 2500 ft on QNH 1000), What you want (request FIS and MATZ crossing). Brief, to the point and if they want other information they'll ask - but it has only happened to me once, when Solent asked if I was VFR or IFR.
As for the climb, best rate of climb is 79kts in a Warrior, so your 80kts sounds perfect. However, it's normally a good idea to do what the instructor tells you - but if you don't agree, ask!