Inherited Pests

I have just moved house and inherited a lovely little garden packed with fruit trees and bushes. Thus far I've harvested redcurrants, whitecurrants and plums. The problem is that a few of the bushes seem to have problems and me being new to gardening I'm not sure how to tackle them all, nor if they are all caused by the same pest. I think I have gooseberry sawfly as the redcurrant and whitecurrants were just dangling jewels on sticks, not a leaf in sight. I think there is a gooseberry bush, judging from the leaves and the little bud-like gooseberries - but they are not developing into gooseberries at all, some of the buds are enlarging slightly and turning purple with mold spots, others staying the same. Then there is the greengage tree - lots of the fruit fell before I realised it was greengages and not unripe plums (!) and know I'm wondering if they should have fallen so early (from July onwards) and if they have a pest too - there are lots still on the boughs that I can't reach that are turning brown and splitting. Or perhaps they are just overripe...

Besides this I have one successful plum tree, for which I'm thankful! There are two trees at the back which are supposed to be pear and apple, which are not fruiting, hopefully they are just resting...

All this in a little garden of a terraced house, the previous owners did great work to fit so much in!

All help appreciated.