Thank you. In terms of some of your questions, the freehold will consist of a freehold title registered at the Land Registry and the constitution of the freehold nominee company registered with Companies House. However neither of these sources of information will contain much if any useful evidence as regards ***** ***** of liability of the freehold company. Rather this will (or at least should) be closely defined within the lease.
The lease will likely (though it should not be assumed) in addition to the structures you refer to above, also provide that the freeholder is liable for maintaining communal pipes not exclusively serving any given flat.
As regards ***** ***** freeholder is liable for the issues depends as you say on the cause. If for example the issues are caused by a failure of a dampproof course then the freehold may be liable, however the freeholder is generally only liable for maintenance of the defined items in a lease. A freeholder is not normally liable to upgrade a building - e.g. same example as above, if no damp proof course was fitted, a freeholder would not be liable for installing one.
As to whether to go to the expense of instructing a surveyor, it seems to me in the first instance, given that the downstairs owner has already obtained independent reports, that it is reasonable for the freeholder to say to the leaseholder that it will attend to any repair issues which are identified and in this respect can it please see the inspection reports as opposed to an editorialised version of them. If this is refused, then the freeholder would need to check the terms of the lease to see if it can pass on the cost of carrying out an inspection to the leaseholder involved - most leases contain provisions along these lines and if so could alternatively ask the leaseholder to make a payment to cover an inspection report on behalf of the freeholder. If it does not and the cost falls to all of you as leaseholders jointly then a decision will need to be made at a meeting as to whether the freeholder is satisfied the issues may relate to structure as to warrant incurring the expense.
Often damp issues in basement flats are caused by inadequate damp-proofing by the original developer that converted the ground/basement flat. Though obviously if it is a leak, then the position will be different and it will be a question of identifying the cause of the leak and establishing whether it is a communal pipe or pipe serving an individual flat.