Well its definitely NOT true that Persian can't climb! They are not terribly athletic, but they can certainly climb, just like any other cat
I think as the spraying is something he's done before at his other home it's just continuing in his new home, and frankly, I'm not surprised if the introductions weren't done gradually. Persians have been unfairly singled out as being bad in the litter tray department, and it doesnt sound as though thats the problem, more likely, as you thought, he's unhappy. Poor boy, he's gone to a new home and literally been thown in the deep end
Is your friend open to suggestions about how to deal with the spraying, like getting some Feilway sprays or plug ins? rescue remedy etc?
Persians should be bathed to keep their coats knot free, but they should only be bathed when their coats are completely knot free, definitely no bathing a coat with knots. However, there is no point bathing without drying in the proper way, with a slicker brush and hairdryer, so not everyone wants to do that. In which case he will need grooming, with a metal comb, every day - thats EVERY day LOL! I only use talcum powder (Simple, unfragranced) after bathing and drying, but it can be used to rub into the coat prior to combing.