I don't know any freelancers that use t and c's, however deciding on some would be worthwhile, from conditions of payment to what you bring to the party should all be detailed, stops any argument.
if you are a contract climber you turn up to their site and work along side them and for them, under their instruction.
you are under their employment for the day. your employer must look out for your health and safety under H&S legislation - dems d rules.
so... if its un-climbable (and clearly so) when you get to site then this needs to be discussed between you and the employer - the result being it isn't climbed - granted, not always that simple when the safety is iffy in your opinion and the employer recons it OK.
The working at height assessment should have covered this. If it hasn't and a mewp should have been scheduled you cant be expected to climb it.
do you still charge him a full rate? this depends on your working relationship. we are all human, we all make mistakes, if he didn't notice the panic fruiting gano on the back of the tree at the time of quoting that's one thing but if he's simply pushing the risks then that another. I think it would be up to you to decide if you follow through with your terms and conditions of charging a full rate half rate or whatever.
just because you have tandc's in place doesn't mean you have to use them.
" should you check for TPO's yourself or trust them to?
If you have insurance but were working along a road and the company you contracted for had no signs and cones or you liable?"
I think these scenarios are only relevant if you are carrying out works as a bonafide subcontractor.
when working as a freelancer its their site and the employers responsibility to organise your days work.... but again this sort of thing is worth mentioning in your t and c's.