Well a voltage pen isn't recommended tbh, but it's better than nothing. Shut the main switch off, the big red one, so there 'shouldn't' be anything live in the house at all, make absolutely sure it is dead before you do anything though, you do not want to assume anything with electrics ... really a voltage tester should be used for that but a pen is better than nothing.
You were correct about the colours, brown is live, neutral is blue and green/yellow is the cpc and 6MM T&E will be fine for a 10KW cooker, that is also the correct number of terminals, you wire each colour to match up with what you see there already, only go in from the bottom of the terminal and lock it down, make sure it's not too tight as you don't want to break any of the strands and make sure you haven't lost any of the copper strands on the likely multicore flex (the wire will likely already be stripped and ready to just wire in anyway).
I would personally prefer a 10KW cooker on a 10mm cable with a 45a breaker, a 10kW load can pull nearly 45a if working at full power, however in the real world, a 32a breaker with a 6mm cable will probably be fine, all that would happen if it did pull more than 32a is the breaker would just trip, the cable would be fine as it can handle more current than the breaker, still you 'might' get nuisance tripping ...if you do, this is probably why.
I assume you will be using the 6mm flex that is already wired into the new cooker, and simply wiring that into your wall box?
I am as near as you have right now to an 'actual electrician' I think. I have a certificate in my draw that says I passed the 17th Edition wiring regulations exam anyway, so I can wire a cooker in
My main concern though is that you make absolutely sure that the circuit is dead before you do anything, it's no good just to assume and I do not trust those pens really. If you test the pen on a known source, then check the cooker circuit and then check a known source again I'd be ok with it. But how are you going to do that with the power off ? ...you see normally you would use a voltage tester with a proving unit. You have to be sure that the pen didn't fail during the test, hence checking again before you start work.