For the Engineer, the duration affects:
> Cryo Blast freeze duration
> Sabotage's hack duration
> Any duration of your bonus power, if any
That's it.
Duration does not affect:
> Incinerate's burn duration (it is always 3 seconds). I don't think it affects rank 5's Burning Damage either; I think that is always 8 seconds.
> Overload's Neural shock duration (and even if it does, it is too short to notice)
> Sabotage's Tech Vulnerability duration (it is always 8 seconds)
Not sure if it affects Sentry Turret's Cryo Ammo freeze duration which is listed at 3 seconds. I think it is always 3 seconds.
As long as you are doing all the side quests, you should not have much trouble with your reputation. Most of the sidequests give you reputation bonuses. Talking to people can also net you reputation bonuses. For example, when Liara is crying in her room after Thessia, talking to Tali nets you some reputation.
Damage is always better on the Engineer. I only ever took duration once, and that was because I used Cryo Blast and Stasis as 2 of my three powers (the third being Combat Drone), which benefited from duration not damage.