The only impact time has is in your final score - the faster you complete the game, the better your score. It's just one element, however, and unless maximizing your score is important, I wouldn't worry about it.
As for enemy strength, all enemy stacks are created when you create a new game. The strength of the stacks, and their composition, is somewhat random. The only element you control is the difficulty level, which will directly impact the strength of the stacks (IIRC, Hard = 30% tougher, Impossible = 70% tougher).
Enemies do not change at all as you play the game, but your own army will - enemy stacks that show as "impossible" or "lethal" at one point may show as "weak" later in the game when you're running around with a significantly more powerful army.
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