D D - it is very much legal advice you need here and you should rely on your own conveyancer to guide you through the legal and registration requirements.
However in an effort to try and help in general terms I've done my best to answer your Qs
- Three key stages 1) application plus supporting evidence to confirm the legal requirements re the claim have been met 2) a site visit by Ordnance Survey to see what the reality looks like on the ground and 3) wider checks and notifications with adjoining or actual land owners to see if they consent/object to the registration claim
- Rough timescales are 1) several weeks unless their application is expedited due to the onward purchase in which case 2-3 weeks 2) OS visit 2 weeks between request and report and 3) 3-4 weeks. As you state timescales will vary depending on complexity but can also be stretched if each stage is not passed seamlessly. So as a very rough and best estimate you are looking at a minimum of 8-10 weeks from it being expedited - and that's a very best estimate
- Expedition - yes but expedition does not hasten Stages 2 and 3. They can't be rushed or chased and are very much dependent on OS and recipients acting as appropriate
- Recommend - ask the seller's conveyancer to confirm expedition and then to keep you informed re progress form there re the key stages. They can track progress re each stage being reached/passed. And do rely on your own conveyancer for advice re exchange/completion and timescales