I believe that the freeholder of the majority of the Swanage Branch is Dorset CC or its successor who will be a statutory authority. I'm uncertain that Network Rail can actually compulsory purchase the property of a statutory authority. In reality these sort of things would be agreed between Network Rail and the CC. If you were able to progress the compulsory purchase you'd need planning permission, a Transport & Works Order which assuming there were objections to would require a public enquiry, engineering and enviromental assessments. Either way it would take years to progress and require £ millions up front before a wheel ever turned.
Yes Dorset Council is the freeholder of the majority of the branch (up to Northbrook Road Bridge Swanage) and Swanage Town Council are the freeholder of the remaining section in Swanage.
I can see no reason why there couldnt be a TOC operating a diesel "normal" service year round and Swanage railway operating a steam heritage service as and when it wishes say daily from end of March to end of September and then Not Monday Friday in October.
Obviously there are issues to be resolved (signalling, dispatch, customer service, fares and ticketing etc etc) but the greater good should prevail.
There is no reason why Network Rail would have to purchase the freehold. They could simply agree some form of access agreement with the freeholder.