The council planning office usually give really good advice, even if planning isn't needed (though I suspect it is in this case). They can also tell you whether it does need planning permission.
Deffo get your own surveyor.
If they are building on the party wall, they need consent. Usually, they would be required to 'step in' back from the line of the party wall within permitted development.
At the very least, photograph every inch of the party wall on your side so that if they cause damage you can prove it. Send the photos to them in a document and ask them to approve them, sign, date as accurate and fair. They can come and look at your party wall if they want to satisfy themselves that the photos are accurate. (But your own surveyors' report is better.)
You are entitled to ask for lots of details.
Ask to see builder's or architect's plans and refuse to grant consent unless you see them.
Ask how they will deal with the weight of the new dormer - this should be on the plans.
Ask to see their insulation plans.
Ask who their Building Control company and named contact are. Then get in touch with them and make sure they're not lying!!
Ask how they will deal with existing and new gutters.
If there's a shared chimneystack, ask how they will safeguard that during works, and what remedial works they will put in place for this stack if needed. Chimney stacks are often sources of leaks.
I say all this as someone who did the dormer, but I did it properly, with my neighbours, and we had no issues at all.