My bike features a Shimano Acera 9x3 gear shift system. My front derailleur is off and I'd like to upgrade it instead of just adjust or replace it. Can I replace it with a front derailleur of the Alivio series?
OK, they work with the same shifters and the same chain, but they are NOT all compatible with your frame. FD-M3100-M is front pull while your FD is down pull (at least it is mounted like that).
Most FDs are dual pull, that means both top pull and down pull is possible.
Altus FD-M2000-DS3 FD-M2000-DS6 (down swing)
Altus FD-M2000-TS3 FD-M2000-TS6 (top swing)
Alivio FD-M4000-DS3 FD-M4000-DS6 (down swing)
Alivio FD-M4000-DS3 FD-M4000-TS6 (top swing)
are dual pull. Your hard tail should be accommodate both swing (low clamp/high clamp) versions. You currently have top swing (low clamp).
So yes, you can go to Alivio, but be careful which piece you buy. There is not just one Acera and one Alivio.
Yes you could, but there is really very little to be gained. The function is the same (I assume both are supposed to be 9 speed, from your description) and the weight difference will be a few grams. Both lines are relatively low-end so not really an upgrade. And even if you upgraded to some old Deore XT(R?), there is very little to be gained by upgrading the front derailleur in general. They are quite crude instruments and the rest of the drivetrain remains the same (including the shifters).
All these are considered equivalent for the front drivetrain compatibility by the Shimano Compatibility Chart
FD-M4000-TS3 FD-M4000-TS6 FD-M4000-DS3 FD-M4000-DS6 FD-M4000-M FD-M3100-M FD-M3000-TS3 FD-M3000-TS6 FD-M2000-TS3 FD-M2000-TS6 FD-M2000-DS3 FD-M2000-DS6