Well, if you'll remember, they weren't supposed to be in that year at all - they were supposed to be in what, the 80's? In UNIT headquarters, anyway. It's been a while since I saw Pyramids, so I'm a bit fuzzy on little details like that. (But not Sarah being awesome with a rifle - I'll remember that for years *L*)
Anyway, back to the main track. It's my theory that the Doctor's TARDIS is sensitive to...well, call them 'knots' in timespace. Places that need intervention. And she takes the Doctor there to intervene, and that's why his piloting often sucks. (Barring Time Lord intervention, randomizers attached to the TARDIS, etc.) When she doesn't have that imperative to get the Doctor to the right point in space and time, she's quite cooperative about going where he wants to go. And since she knew he wasn't going to leave Sutekh to have his way, she let him take them to the potential (yet at that point in time, actual yet preventable) future.
The way the Doctor showed how not-human he was every so often, that's what I miss about the new series sometimes. There are some moments, yeah, but overall...too much of him pretending so as to not scare off his companions too soon.
As for 'I walk in eternity'....I have no clue. Sorry on that one.