What's the problem with my car's acceleration?

Okay I have a sever problem and I am unsure what to do about it. So I own a 1995 Subaru Legacy LSI 4 Door Sedan. As of the last yearish when I go to start my car it starts up fine and the RPM's go to 1.25-1.5 upon staring up and fluctuate between .70-1.0 as it "warms up". I have never had to warm up my car before before the last year. It used to turn on and I could go. But now here is the issue. When I start my car and the RPM's do their thing. If I give it gas during this process the RPM's drop to 0 and the car acts like it's not getting gas and is about to die. (hang in there this may be long). So if I let up on the gas pedal the RPMs go right back to normal and I have to wait for about a thirty seconds then I can give it gas and it doesn't do the 0 thing. Well when I let it heat up to any degree and try to go, as in put it into drive and then start giving it gas its a hit and miss on the first 10 seconds of driving, more often then not it lags as if the pedal wasn't pushed. I actually have to put it to a certain degree when I push the pedal it seems to get it to register to go. Or it doesn't register the RPMs go wild kind by dropping to 0 again as I am trying to move. I describe it as (by the way my car is an automatic) if you have a manual and you let up off the clutch to a certain point and the car starts to move a little but not much. it's that kind of thing in a automatic at first. Well anyway if it does go and I make it to the first stop sign on my street (I am not saying it dies by saying if it does go) I stop the car like I should. But as soon as I try to go it acts like I have just described. The first stop sign is about 200 feet to 400 feet away from my house. Well if I rev the engine up the RPMs don't go up like they shoot instantly they stay as if I didn't give it gas.... Well when I continue past the stop sign and it starts going 25-30 miles an hour like a normal car should reasonably by the time I get to the next stop sign and stop and try to go again it does exactly the same thing as before. Which is another oh 500-700 feet away from the first stop sign. Well when I travel from there to the light which is about a third of a mile away it will do it again. Usually after this time it doesn't do it again until I leave the car sitting for awhile and then go to start it again and the process repeats and seems to get a little worse over the last year.

Well recently as I was driving and I picked up my wife from her work about 5 miles away when I went to start the car again after I got there it wouldn't want to start acting as if it didn't have any gas. Well it thankfully started and I got almost home and the car died on me as I was driving. After examination and getting it retro towed home by my brother in law we found that the pump had went bad. I thought that fixed the problem but it didn't. the car runs again and gets gas to it but it's doing exactly the same thing as I already described.

here is what I have done already tests and new items on the car. And I am totally stumped on this one.
1)changed the spark plugs about a month ago. Had a little effect on the car and made it run better to a certain degree.
2) Changed the fuel pump after it went out. There is no change in how the car runs though as described above.

3) I tested the throttle position sensor and the readings are what they should be. today I did this

4) Tested the knock sensor and it was what it should be.

5) My brother in law came out to help and he unplugged the AC power in the engine. There was a noticeable difference in how the engine ran. I test drove it after this (all today number 2-5) and it's still doing exactly the same thing.

To note today and yesterday the car has started to do it every single time I stop and go just not as bad as the first three stops I described above.

I just don't get it why the engine starts up fine and when in Park the RPMs go up fine when I give it gas after the first 10-15 (not 30 as stated above just lazy not fixing it) seconds the RPMs act normal. But when I try to drive the engine acts like I haven't even used the pedal and when it does register I have to have it at a certain degree (not temp) on the pedal and then it works kinda. the car does not jitter or stall rump or whatever its called. It just won't go.