1. How do you think the Order came into existence after the Entity's spaceship crashed? How much time could it logically take for a medieval world to change so much and incorporate all the technology?
Almost immediately, with unexpected speed. The sentient virus is implicated in the hearing of voices, as it is the infected survivors who found and control the Order. The Entity communicates through the "virus" (which is likely nanotech based rather than strictly organic) and uses it not only to influence people in its search for the Sigil and desire to feed on life, but also to communicate its knowledge of advanced technology to those people to further its ends. This dramatic technological revolution results in a world of castles with computers embedded into their stone walls. Architecture and culture could not keep pace with it; it was, in effect, a technological singularity.
2. How did the spectres of the Sigil come into existence? How and when was the Sigil created? And how was it distributed to the Order generals?
The beta strings of the Oracle's dialogue, as well as subtle hints hidden throughout the game world, reveal that the Entity itself and its offshoots, the Spectres, are beings which originated on the same world. At some point in that world's history, they and others created the "sufficiently advanced technology" and were then exiled into space, sealed aboard the vessel that was later called a comet.
The exile of the Entity was evidently a cataclysm-level event, as it left most of the ancient civilization in ruin (see below). Thus by the time Strife takes place, the world's cultures had only advanced as far as a stage roughly equal to medieval Europe.
Amongst the subtle evidence in the game regarding this are the Mayan-like ruins areas to which the Spectres and the Oracle instinctively gravitate, which additionally bare upon columns inscriptions in the exact same Mayan-like hieroglyphic language which appears inside the Entity's space ship.
The Sigil was the key used by the ancients to seal the Entity into its ship. You might conjecture that the Sigil fragmented when the ship crash-landed, and this damage to it was responsible for allowing the Entity's poisonous influence to leak out in the first place. In order to see to collecting the pieces back together, the Entity sent out the Spectres to possess individuals with an overwhelming desire to find and assemble the Sigil.
3. Why didn't the spectre-possessed Order generals simply convene, assemble the Sigil and free the One God, as each of them separately wanted to do? I know that Macil and the Oracle weren't of the Order, but their spectres' goal remained the same.
Problem is, human selfishness and greed seem to have played some role in hampering the Entity's designs, for, though the Order possessed all five pieces amongst its adherents (if you believe Macil was always allied with the Order, at least), they kept it separated and came to a sort of balance of power between the leaders which might have gone on for quite some time longer had the Front not intervened.
4. How and when did Macil get in possession of his Sigil piece? Was his allegiance strictly to the Order, or did he try to struggle with his Spectre and simply fail to resist its influence?
Open questions, and any answers are going to be speculation. It was intentionally left this way by Rogue. In my opinion, Macil probably started out good and was corrupted after the Castle strike when the Programmer's files decrypted by Feris gave him knowledge of the Sigil, which he admits to knowing little of until then ("we have reached the limits of my knowledge; seek out the Oracle").
However I've also seen BlackBird's assertions about him taken at face value by some Strife fans, whereby they see Macil and the Oracle as two different splinter factions from within the Order, both seeking to assemble the Sigil for their own purposes. Through the player character, these two splinter factions come into direct conflict with each other, driving the main choice you have to make in the game's plot.
Believe what you want, ultimately. I prefer Macil as a tragic character, a good guy turned bad by the Entity. His impassioned speech during the game's intro is what gives me no choice but to believe this about him.
5. Why was the One God imprisoned in its spaceship in the first place? Was the creation of the Sigil just a plot for it to go free? Why was it imprisoned in a spaceship with keyholes that it didn't readily have a key to open?
The Sigil was part of a seal to keep him in the ship; the game's pretty clear on that when you take everything into account. It was imprisoned because, clearly, it was a terrible evil in control of "magic"-level technology - a world-ending threat bent on absorbing all life it can absorb and destroying whatever it cannot.
6. If the Sigil was already there in the spaceship, then why didn't the ones who found it first use it to free the One God immediately? Why did they separate it into pieces and distribute them to the Order's generals, only for each one to later strive for the rebuilding of the Sigil anyway?
I think I may have answered this already. I don't think the Sigil *was* all in one piece but was already fragmented. For that matter, it's entirely possible and would make a lot of sense if the Sigil wasn't even ON the space ship but its parts were relics that had been long hidden on the world itself.
This makes more sense when you find the beta dialogue of the Oracle, where he states explicitly that the Entity and Spectres were ancient inhabitants of the very same world. I do not understand why Rogue made this less explicit in the final game as released, because as a result the game's plot makes less sense.
7. What of the rest of the world? The remaining continents, not to say countries?
Epic stories must always be myopic in scope for the sake of not taking forever to tell. From the reaction of the Front, it is clear that the Order is a global threat to mankind. I'd assume that by the time of the game, the conditions in Tarnhill of slavery/serfdom/peasantry had become the predominant way of live in all civilized areas, and the Order was slowly sweeping through what few free lands remained.