what it looks like to me is you've bought a cheap shit run a round and its cheap and shit now you're complaining?

mot states that the car was in a safe usable condition at the time of the test

the two things you pointed out the rad and the tyres suggest the car and been sat around for a while

the tyre pressure could have been low been mot'd passed and then inflated and cracked or the car could have had other wheels on for the mot

the rad tough shit not an mot problem and not a seller problem if it split on the way home

as for the brakes there's no excuse, but if the hoses where wrapped up neatly enough (so the tester didnt notice) and the brakes past the brake test then thats

i would say your problem is with seller not the test station next time take a competent person with you to look at and test drive the car.

just get it fixed sharpish and learn a lesson