What is a reasonable Disable traps skill at level 8? My Thief has a '4', and is an expert, and I don't think I've disabled one yet.

Does Perception contirbute?

I'm not sure about Perception – it may only govern trap detection – but Disarm Traps is one of the priority skills for my zhief to avoid traps in dungeons being always one step (i.e. a skill point or two) higher than my thief. With a high enough skill you can disarm most traps without getting damaged, but there will still be traps where nothing helps, and which deal a disproportionate amount of damage considering the value of loot stored in the container. To be on the safe side, always make sure all your characters have a full HP bar before attempting to disarm a trap.

Get master ASAP. Otherwise search for items boosting disarm skill, or enjoy blasts in your face.

It seems that the random element, if there is one, is pretty small. With a 5 skill, I literally NEVER succeeded with a chest while clearing the trogs in the dwarf mines. Out of probably 100 tries (reloading of course). With a 6, I literally suceeded every time.

I always have a thief in my party for this very reason. Master Disarm is available to an unpromoted thief. For my thieves I allocate all skill points toward disarm and liberally use horse shoes by traveling to all the stables.

Some traps to really look out for are those in the Haunted Mansion, in the Barrow Downs. You need master training, with at least nine ranks if memory serves. Once you grand-master, though, you will never fail again to disarm a trap. And you don't need any items to increase your skill rank then, but up to that point the items help and the degree of skill training makes a big difference itself.