unstable idle, engine stalls, horrible gas mileage. please help?
 

Ok so lately, my 04 mazda3 2.0L has been acting weird. Most times, it'll start but rarely it has issues turning over. My gas mileage recently dropped from about 340mi per tank to about 260mi per tank. My a/c belt and clutch are off, which allows my car more power, but it should not drop my gas mileage that bad. Same with the new winter blend gas I have to use. It should drop it, but not by 80mi per tank.
Anyways, last night my boyfriend and I disconnected my battery to install new HID headlights. Now, all of a sudden, if I drive my car about 4 blocks the idle will jump from 1000rpms to 500rpms and it'll continue to jump until I drive. If I ignore that and continue driving, my car tends to stall at stoplights. If I brake too hard and too fast, the check engine light with flash on for a moment then turn off. When my car stalls, my battery, check engine, power steering, and engine oil lights come on.
About 5,000mi ago (currently 95,000) my car started stuttering when I try to take off. There's a moment of hesitation. It also shifts kind of hard from 1 to 2 gear.

Does anyone know what's wrong with my car? I'm incredibly worried about it and I can't drive it because of this and I drive 100mi two days a week to school, so I'd like to get this resolved asap. Thanks.

Why remove the A/C belt? If you never run the compressor then it's just going to seize up whenever you hook it back up. I can't imagine the power increase is quite that much.

Have you:
-checked tire pressure/treadwear
-air filter
-throttle body
-MAF sensor
-battery contacts are clean and tight
-engine mounts (specifically the passenger side one)

can you get the stuttering/fluctuating idle to reproduce by playing with the MAF harness? Were there any mods/changes which immediately preceeded the mileage decrease (other than winter gas)? It's not uncommon to have some change in idle after disconnecting the battery since that resets the computer. It should settle down within a couple hundred miles.

What do you mean your clutch is "off"? For the shifting have you changed the MtX fluid?

Check the MaF sensor for broken wires. Wiggle the wires while the car is running