I'm tending to think that it might be a type of aphid thats the cause of the problem with the plum tree
This may explain the sticky covering (known as 'honey dew') and also the feathery deposits which could be where the aphids have metastasized into adults, leaving their skins behind them.
There are various sprays on the market, thet you might want to check out that can control aphids, some folk swear by a little washing up liquid mixed with water in a spray bottle, it seems to be having some effect on my courgettes.