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On a serious note you should consult a party wall specialist. Not to cause trouble or anything like that but it has the potential to make life easier for both you and your neighbour in the short term if the process is handled formally. Also it could resolve future problems for either you or your neighbour in the future, if one of you sells and the new neighbour decides the boundary line is not right it could be a real arse ache for the one of you still living there.
Bobbo-
the line of junction notices don't really give you the option to appoint a surveyor at their cost, in the same way a party structure notice (or adjacent excavation notice) does, so you'd be paying their fees.
you can consent or not - as dan says, below. watch costs, as it you consent, they may try and attribute some costs to you, as they are technically providing the boundary fence.
they can put the foundation of the wall on your land, as long as it is not a 'special foundation' (ie - reinforced concrete). there is nothing in the act that allows them to do that - they need your permission.
happy to discuss via pm.
BRM
I imagine it'll be like it is now, with the fall to front and back not to the side. If it does fall to my side however, I'll collect the rainwater.