Firstly, I think you need to check the extension has been built according to the planning permission that was granted, so many people overstep the regulations which leads to situations exactly like yours or worse. You could consider asking the building inspector from the council to come and take a look, I certainly think that things are not quite right.
Get a written quote for replacement of the damaged slabs, plant posts etc and present this to the builder and a copy to your neighbour advising each of them that the other has a copy. The very least they should do is replace your broken slabs like for like, a bodged repair with cement is not acceptable.
Also, can you lock your property whilst you're out at work to prevent any workmen accessing when you are not at home? Alternatively, you could consider putting leave in and being at home when they next come to do any work and watch everything they do.