Purlins never used to go completely though the party wall, do they even now? Not a problem, are there enough struts?
Old rafters always “belly” dosn’t look that bad. These are machine made tiles not handmade, they look good no frost damage at all.
No undercloak on the verges, not great but not a problem just roofer being lazy. One tile missing under stack, tile fillet around stack will cause issue one day, it should be lead.
Hip ridge need repointing.
Bottom of both verges at gulley where the houses meet have been repointed suggesting work done to lead/felt, i’d check that to see what they have done
I’m a roofer BTW