Time of War will work. You'll need to disallow and modify some of the Life Paths that don't exist during the era you're playing in. For example in 3025 you don't want to have FRR or WoB characters because those factions don't exist yet. Era Report 3052 talks about some of this, and provides adjustments for Life Paths and says that it can be used for characters from 3025-3052, though some common sense might still apply.
The gear section is already set up to give you ratings for equipment in the Succession Wars, so that shouldn't be a problem.
Other than that ,I'm not sure there's anything else that's era specific in ATOW.
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To answer about the tech question...Yes, there is. But each piece of tech comes with availability ratings, which will let you know if its available during the Succession Wars or not.
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