The air conditioning you can certainly do something about, I really think just talking to the occupiers above and explaining the situation will sort it out. They probably don´t even realise it is affecting you, what´s more they could have paid a contractor to do the work for them and assumed that it had been done to a sufficient standard.
His outbuilding is a bit trickier. I mean honestly, to what extent does it bother you? I live in an area where people are adding 2 storey extensions, garages, walls double the 1 metre height limit, and really, everyone just gets on with it. The town hall turn a blind eye in 99% of cases, it is only if they receive an official complaint that they act, and even then the culprit just has to pay a small fine for not having had a permit for the construction. I´ve never seen anything torn down.
This is Spain and many people regard the land they´ve bought as theirs to do what they like with. I´d make a bit of a fuss about the water dripping from the air conditioning if it bothers you, but unless his outbuilding is in someway obscuring your view I´d let that go.
I have a neighbour who has had guttering fitted to his roof, it´s so poorly done that when it rains the water splashes our side as opposed to running away through his downpipe. My wife made a Jamie Oliver herb garden directly beneath and really, we´re chuffed to bits.
I´d try to avoid dragging lawyers in over something so petty. It would be expensive, probably get you nowhere and make you a pariah if you´re living amongst natives.
Good luck :)