To the OP
In no way is this meant to sound rude, but if you don't know what the problem is you aren't really qualified to tackle the task in hand and, for your own protection, avoid this like the plague.
From the photos, it looks to me like the clearcoat has marbled, in which case cutting and polishing won't do too much good. if it is clearcoat failure then then only solution for an A1 job is to remove the clearcoat and re-apply it - i.e. respray time.
As has been said by others, a car that's worth a few hundred quid isn't really a prime candidate for a job that is likely to cost 5 times the value of the car. The owner clearly isn't sentimentally attached, or wouldn't have let the car get to this state in the first place.
If you say to him you'll have a go, will he be expecting a 10/10 job? Is he going to be an a55hole if you don't get it up to scratch? If so, I'd give this one a wide berth old chap...