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 For your peace of mind, and to help any legal case later on, I'd suggest that you get your geometra to carry out a full survey and provide a report [inc photos etc] of the 'party wall' before works starts, and follow up with a full survey after works have finished to determine any effects the works have had on the property.  [In the UK this would be at the cost of the developer, but I don't know how its funded in Italy] Give the 'other party' a copy of the initial survey/report before they start so they know what the condition of your building is, and give them the opportunity to carry out their own survey if they want.  Keep them updated via your geometra - don't deal direct with them.  You may wish to consult a lawyer before work starts Good luck

Definitely get your geometra to make a record of the condition of your house before the neighbours start work. If something becomes difficult during the build, remember that the first point of contact for 'public oversight' is your comune, probably the polizia municipale (vigili).They may require you to complain in writing (a denuncia), but equally likely they'll just do a drive through to see how the site is behaving, and act off their own bat if they don't like what they see (on safety, interference with the neighbour, or untidiness grounds: I'm not sure they have the authority to have an opinion on build quality). Good luck

Taking into account that the geometra already has a few injunctions, it will be important to make him feel that he is carefully watched.