The damp could be something or nothing. My advice is the surveyor will have likely used a damp meter - they are useless.
Low level damp maybe due to the guttering issues, or could be due to the ground level outside being higher up against the stone walls. To solve the former, fix the guttering, the latter something like a french drain would work.
The asbestos is more backside covering. Unless you know exactly when the covering was applied and what was used, the asbestos is a bit like the Japanese Knotweed issue - all a maybe.
There is nothing on the info you have provided so far for the age and construction of the house which would worry me at all. Old houses, in fact all houses, need maintenance - it is the joy of owning a house, especially a period one.
If you really want to know exactly what problems there are or are not, ask a surveyor who is used to dealing with period properties of a similar age and construction. Once the survey is completed as the question, would you buy it. If they say yes, all is good, if no then walk away.
Periodproperty forum is a good site to visit, and already mentioned on here SPAB have some useful information available, especially about damp.