I have lots of why the Avenger is a poor choice, but not a lot of why something else is a better choice - so let me put my two cents in here and hopefully be helpful.
This is the most telling (to me) comment you have made so far.
Brovikk Rasputin wrote...
Well, I sure kill a lot of enemies with it, so what's the problem? I'm an Adept, so it's only for when my powers are recharging anyways.
You should not be 'killing a lot of enemies' with your weapon. You are an adept YOU are the weapon. Every weapon you could possilby equip on your character should be a total after thought - used for snap opportunities or OMG moments you need a get out of jail free card.
The heavier the weapon the slower your biotic recharge times will be. So by takin gin an Avenger - assuming it's impacting your cool downs - your hampering yourself. Your biotics are FAR more powerful than that gun and you should be slamming them out so fast that you barely get to see the cool down timer doing anything BUT cooling down.
As mentioned before - your playing a squishy class with a class of gun that requires exposure and particularly one of those guns that requires a LOT more than others. If your spamming warp ammo - an SMG is a better choice. If your spamming tech ammo (Cryo, Incendiary, Disruptor) STOP - they interfere w/ your biotics.
The carnifex and other heavy pistols like it rock because they deliver a ton of hurt w/ minimal exposure and are light weight - they also synergize often w/ adept classes (pistol weight reductions etc) Im not a fan of the scorpion because of the delayed detonation - if i need to use a pistol on a biotic - i generally NEED it to hurt right then and there. my preferred go to is my Talon 7. I know not everyone has that (Why don't you make your manifest public so we can assist w/ more detailed build info?)
Gear/equipment wise - again - we have no idea what you have - i'll give you an example of a typical load out for me w/ my Asari.
Weapon: Talon 7, Carnifex 10, or Paladin 5. (paladin is the carnifex w/ fewer shots more punch per shot, and is heavier (well for me thats true since it's 5 vs 10)
Mods: If i don't get a 200% cool down bonus - im going to run ULM If I do get 200% cooldown:
1) Armor Piercing - i don't ever NOT choose this
2) Heavy barrel - i dont shoot it enough to care about extended clips - i want massive damage.
Equipment:
Ammo - Warp 3 or 4 (for gold or platinum you roll w/ the good stuff)
Armor - Power Efficiency Module - i want to cast FAST
Weapon - Pistol Rail Amp - again - i want to hit fast and i don't care about accuracy - not going to try for a head shot - i am trying to kill whatever snuck up on me, but i can STILL shoot the head if there is time.
Gear:
Commando 5 - Boost to biotic damage and pistol.
You wont get kicked w/ a similar load out for any VALID reason. (N7 Rank kicking is foolish if above 120).
Now - you should be going in with an adept when there are other adepts present - preferrably of a different type - good synergy can be had with the Justicar, Fury, and Drell (off the top of my head) those classes are excellent 'primers'. Watch for glowy blue bad guys and throw at them. watch them explode - watch for more glowy blue bad guys - repeat. This is the adepts bread and butter style of play. You can do the same thing with warp/throw - but sadly - your not going to do it as well as you would w/ a buddy. (time)
Do not use stasis bubbles on elite units (Banshee, Brute, Atlas, Prime) or turrets - it does absolutely nothing to them. Stasis bubbles are fantastic against Phantoms - spam it all day long on them and your team mates will love you.
Stay in cover.