I haven't seen the submissions from Sandie Peggie or NHS Fife, so this is little more than a guess based on knowledge of how these things work.
Starting with NHS Fife's applications...
Restricting disclosure
The basic principle is that you must disclose everything relevant even if it is harmful to your case. There has been a previous disclosure order, but they have failed to comply. Getting it restricted at this stage will be very difficult for them. They will have to convince the tribunal that the disclosures previously ordered are excessive and/or irrelevant. Given that there has already been an order on this subject, they have already had their chance to make these arguments. I would be surprised if they succeed to any significant extent.
Restricting public access and excluding Tribunal Tweets
Given the principle of open justice, I can't see them getting very far with this. I suppose the tribunal might agree to some restrictions given the problems there have been with the video feed, but I would be surprised if they succeed in excluding Tribunal Tweets. If they did, that would be very appealable in my view.
Looking at Sandie Peggie's applications...
Adding Kate Searle as a respondent
The difficulty with adding her at this stage is that it could cause significant delays. She may want her own defence rather than joining in with NHS Fife and Upton. If she does, she would need time to appoint a lawyer, and they would need time to get up to speed with the case. And they may want to cross examine some of the witnesses who have already given evidence, which would have to be allowed. So, although I may be wrong, my expectation is that Kate Searle will not be added, although it will still be open to Sandie Peggie to take action against her later.
Forensic examination of Upton's phone
On the little we know, this would seem to be the application with the best chance of success. Provided NC made a decent case as to why this was needed, I can see this being granted.