Do you have to use the mot inspection sheet now

you can use your notebook if you find it easier, although I personally prefer to use the inspection sheet for the one reason that it has all the vehicle details and the time of test etc that I can attach to the emissions printout.
It is entirely up to you   

You don’t have to use either as far as I’m aware , stand to be corrected though

well said,as a for instance when you get a motor in that's saturated underneath fuel/shock/brake leaks are almost impossible ta assess or even see,i note it on my list but don't see any point entering it as an advise,staple to your emissions and keep for 3mnyhs,aint compulsory but can save your ass

Found this in the updated MOT Testing Guide.

If testing under CT, you must calculate the brake efficiencies and retain the readings for later data entry. You should record all results on the VT29 and retain any printout. Refer to the MOT Testing Guide for a full explanation of CT procedures.

pretty much any paperwork you keep is 3mnths,sheets,emissions etc