RE: Scarfell Pike
I have to say I agree with the others about the legality of cycling up there. I'm sure you wouldn't be the first though.
Helvellyn and High Street are both bikeable - Helvellyn is the 3rd highest in England, only 25m lower than Scafell Pike, and it's legal and an epic trip, There will be a fair amount of pushing/carrying to do (although I would think a lot less that Scafell Pike), but a bit of research on biking forums would get you better advice on that.
There is a legal path from Borrowdale over to Wastwater, which goes round Scafell, but I think you'd end up pushing most of that too as it's not a great path.
Whatever path you take, it might be worth walking it before you cycle it, to see how much riding you'd actually get. It might also help you avoid getting lost at speed on the way down.
Think about your sentence "I'm pretty much a novice when it comes to mountain climbs" - If that's true, then I'd also question the safety of going up any of the big tops without some support who know what they're doing. On most of the hills you could get significantly lost, never mind the consequences of a fall etc.