the spots on the branches is lichen, the yellow spots on the leaves is rust, the all yellow & brown is just from age & the sun, this happen a lot with frangipani/plumeria. I have several hundred growing here( I do a lot of cross pollination work to create new varieties, one of the reasons I moved to Thailand) and have the same thing, the hummidity in Thailand is the cause of rust & lichen, with more rain and heat it keeps happening. There are treatments but it is hard to control rust, lichen causes no damage to the trees so its not really a problem, leaves start to yellow and get brown edges etc as they age and the trees are getting close to dormancy/their natural rest period, many of mine are currently doing th same thing, they will start clawing back up again(new leaves) before too long, its just a natural process they go through each year