Without wishing to sound facetious, your unfortunate situation sounds exactly like a question I answered in my Planning Law exam for my Masters. Now here it is in real life! The short answer is, there is often no 'right answer' to a situation like this. However, I'll try my best.
My first suggestion was to have been to get a solicitor well acquainted with planning law. As you have a solicitor, I can only emphasise the need for planning law competence. It might also be worth your while to talk to a planning consultant. The IPI website (http://www.irishplanninginstitute.ie)
, though not exhaustive, should indicate whether there's one in your area. A competent architect might suffice for this either.
Whatever works your neighbour has carried out, if they were completed more than 5 or 7 (see below) years ago they are outside the statute of limitations for enforcement proceedings, even where they infringe on a public right of way.
From Dublin City Council website:
"Under the Planning and Development Act 2000, if the development commenced on or after the 11th March 2002, the time limit is 7 years. Action must be taken within five years if the unauthorised development/use commenced prior to that date."
The burning of rubbish is a different matter, though, and could be legitimately investigated under planning law as it might constitute a change of use, if there is no permission for such an activity (as seems likely). However, I would caution against fighting fire with fire (pardon the pun!) at this stage, as it could have serious consequences further down the line. It would be best first to sort out your situation on its own, without recourse to the 'he said - she said' school of argument, if at all possible. If the burning is still an issue when this is resolved, perhaps pursue it at that stage.
Their conclusion re the 12 sq.m. at first floor seems correct for a terraced house (see http://www.fingalcoco.ie/YourLocalCouncil/Services/Planning/DevelopmentExemptFromPlanningPermission/InformationRegardingExemptedDevelopment/
for general guidance).
The boundary wall issue is less clear cut, and I can't quite envisage it from your description. Is it that there is a laneway running alongside your house, with one side of the laneway being formed by your gable end and your garden wall (being an extension of the line of the gable end)? In other words, will your first floor extension form an edge to the laneway? If so, perhaps they have a point, though it's one I can't really clarify for you I'm afraid.
The type of map you are looking for might exist in the Valuations Office in Dublin (I think now located in the Irish Life Centre [NOT the ILAC Centre] on Abbey Street near the VHI Head Office). It would be worth a visit, but keep your expectations lowish. I'm less sure about the deed, but would guess that the Registry of Deeds would be a place to start.
Even if it turns out that you don't have the right to build on the wall, it is not unheard of by any means for an agreement, whether by means of sale or otherwise, to be reached between the owner (the local authority) and a developer (you). A look around many Dublin suburbs with garage extensions beside laneways would tell you as much, at any rate.
I hope this is of some use to you. I'd be more specific if I could, but some of your details are a litle confusing. For example:
"He owns two houses that meet the perimeter of our boundary" is somewhat unclear;
"Built a wall against the gable wall of our house"- Not sure how, if one side is a laneway and the other is a party wall as part of a terrace;
"put a roof on an alley way which connects his house to ours"- is this the same laneway as you mentioned re the boundary wall issue?
Sorry to nit-pick, but without drawings or written compass points it is a little difficult to build a comprehensive mental picture of the site.
In conclusion, I sometimes suspect a fear of litigation has led some local authority officers to adopt a hardline approach to matters such as planning enforcement in recent times, and it is possible that you have simply been the 'victim' of a very by-the-book approach. Equally, it is possible that you are the victim of a combination of a vindictive neighbour and a somewhat underhand enforcement officer. In either case, I would again stress the need for a planning savvy solicitor or a good planning consultant. A message board such as this can never really replace good advice based on first hand knowledge of the particulars of a case. Keep an open mind about solutions, and remember to appear keen to resolve the matter in as amicable a way as possible. The behaviour of the enforcement officer, even if technically correct, certainly seems a bit unprofessional, but to an extent it has little bearing on the details of the case, which in a nutshell sound like:
a) you will need planning permission (the 12 sq.m. clause); and
b) you will need to resolve the boundary wall problem with the local authority.
Best of luck with it- I hope it all works out.