So many questions... should be able to answer them though.
Firstly the "media special" would be from T4, the Sunday morning strand of teen shows which Dermot (who later fronted BBLB) hosted. They repeated the weekly recap editions and would usually have a few BB related segments around that and evictees on the show too.
Davina - yes, she just turned up on eviction night for the first time. It was never promoted as her show - the presenter initially was almost an afterthought, though some of the biggest names at the time (Zoe Ball, Graham Norton, Denise Van Outen) were said to be in the running. Davina had made her name on MTV and done Streetmate (a dating show) for C4 which was quite successful and a couple of entertainment formats for ITV. She's also hosted The Brits earlier in the year.
As for eviction shows - yes, the split eviction shows continued for all of C4's run, though the time between them shrunk over the years to eventually be just half an hour. Those first couple of years though where they had around two hours to get ready, pack etc. in between as well as stress about what might be on the other side of the doors really added a much more human aspect to the eviction process, as indeed did the format of the show in the early years with friends and family of housemates really involved too, and indeed Davina spoke to people in the crowd directly too. I've always said when they moved the entire show out in front of the crowds from BB5 onwards the crowd actually became less involved, other than their tiresome chanting and booing.
The classic set up at Bow for BB1/2 though was the best the show ever looked - they never really managed to recreate that at Elstree (BB4 probably came closest, or CBB2 which had a smaller intimate set up). I really hope any revival by ITV looks to recapture that atmosphere rather than the Elstree mob of later years.
Three nominees didn't start till the C5 years (and they varied the rule as they saw fit rather than having a clear nominations criteria) - during the C4 years it was always two up for eviction which saw some great head to head evictions over the years, especially in BB2. I do think 2-3 nominees works best so they are the focus of attention and it's not a case of half the house being nominated, so it's nothing to worry about. Similarly three or four in the final week was always better than the 6-7 later years often had - much more of an achievement to make it to the last week when only a few do and it gave them all a decent amount of airtime at the finale.