The Planet Gallifrey is held in a force field, but existed in real time.. the time war happened a loooooooong time ago according to lesser species.. when the time war happened, a time lock was established, which began in the future of earth say 52nd century, and worked it's way back through time, as the time lock began, it locked all things within the field outside of real time..all the things within the field were locked in time as well.. which meant past events on skarro could only be effected in the time lock.. (time in the past is set, and locked and cannot be changed in the time lock)
the events in the past happened, but are now locked in time, and are not reachable via time travel or tardis.. but as the time lock travels back through history, it alienates the time lords and daleks from their normal time, and cuts off certain time events while also making them fact..
example: the doctor does have a re-pour with UNIT, from his days in the 3rd incarnation..however, the doctor can mess with his former selves cause he himself is not part of the time lock.. were he to become a fixed figure in the time war time lock, he would then not be in the universe to mess with his former selves in the first place..
only his 8TH incarnation is inaccessible, due to his being partly locked in that "bubble" so to speak..
here is where things get tricky.. to me, if the daleks were to say escape the time war, and are not mad in the process.. and one tries to traverse time to the past to warn it's previous brother-en, it would not succeed, because the rest of it's race are trapped in time..the time lock is like a cascade of energy or a web which not only covers the battle and tries to contain the carnage in real time, it travels back into history and loops the battle in time itself..so certain events are locked in the time lock, like the 4th doctor's visit to skarro, but just that event, and it cannot be changed because it would be like a shadow of true reality being that the rest of the universe is held constant by that event.. it happened, but cannot be changed in the time war..
if a dalek were to land on skarro in that time, the fourth doctor and those events would be like watching a movie.. unable to change them..
so events in the time war happened, just sealed off from reality..past events also happened, and are sealed off from reality in the time war..it doesn't change true reality outside the lock, it just makes them begin to fade from memory.. higher species know of the loss as was stated in the stolen planet.. and the charles dickens episode with the Gelf..
lesser species, who weren't aware of the time lords, and daleks as much were oblivious to their disappearance..
as for when the doctor is from?
I think that if you look at the series, the time lords and the Doctor "seemed" in real time were on the same level when the events of omega were going on, and through the time vortex they could have manipulated time and energy..
my hypothesis is that the time war happened in the 55th century, the doctor is from there.. and was forbidden to go into the future of gallifrey, hence the clock in the tardis that shows real time on gallifrey..I think this feature eventually became locked into the Tardis chronometer, and became a standardized time when joining his people..
it makes sense..
Omega's space lightening beam had to start in the far off future..it could travel faster then light cause it traverse time-space.. then after the defeat, the displaced omega then ended up on 1980's earth, and transmat from that time to Gallifrey which existed in the future..
it made sense that the time lords would feel the power loss in the future, and because the 3rd doctor was in the past, they could still send him energy and transpose his former selves..cause energy back in the past still existed for the time lords, and so thus the events that happened in the 3 doctors had to have happened in the future..
this 52ND century makes sense, as the time agency grew up after the time lords faded into the time war..
but because of the time lock their memory fades, and they drift into myth and legend because of it..
Captain Jack remembers seeing Dalek ships before and remarks they were destroyed..
if Abslom Daak is a regular fixture of the universe, it makes sense, he was a Dalek hunter in the 50TH century..
so my bet, is the 52ND century.. fits the universe most In my opinion.
I may have to reflect on this and word it in a better way, it may be jumbled..