Jerks at low revs

Good afternoon, I have a problem with my Toyota Corolla 4E-FE engine, from the year 1997, 5-speed manual
transmission.
1. I start the car cold in the morning, without waiting 1 second (since I usually leave in just enough time, as if waiting for the car to warm up), I start driving and when accelerating or decelerating the car gives gross jerks. 
Once the car warms up, the jerks seem to disappear, but no,they reappear at a rev regime always below 2,000 revolutions, if you even release the accelerator around 2,000 revolutions (maybe 2,200 revolutions) and verified that the car when it reaches just 2,000 revolutions, gives a ***** and continues to decrease in revolutions.

2. Driving while the car is hot, if you keep the car close to 2,000 revolutions (I think between 1,800 and 2,200 revolutions), it is especially noticeable in low gears 1st, 2nd and 3rd, the car jerks. Curiously, once the car passes 2,200 revolutions, it goes fine whatever the gear it is wearing. As if for example in 2º I rev it to 3,000 revolutions, and I let go of the accelerator suddenly, the
car slows me down well without problems.

3. At this point, tired of going crazy, going to mechanics and others, I decided on my own to buy 2 new coils (my 4E-FE engine has a coil for 2 spark plugs and another coil for another 2 spark plugs) and also buy the 4 new spark plugs that the original DENSO car has. The cables DO NOT buy them since they were "new", they had recently been put in place. 

Well, after changing all that, the car remains THE SAME as before, that is, I spent the money "for nothing" or lookingat it from a good point of view, to rule out that this is NOT what the car has bad. I cleaned everything I could see with clean contacts, the 
intake is clean, the spark plugs are new, the air filter is clean, new coils, new spark plug wires, good fluids, gasoline filter (maybe I will change it these days, since I have changed it for a long time, I do not remember how many kilometers), in general the car has its maintenance. I blame something dirty, some adjustment of something or I don't know ...

Please see if someone gives me a hand to solve this dilemma, because the car already has 455,000 km, almost 24 years and in general the car is new, I have a hard time removing it and buying a new or second-hand one, since the car walks and does not leave me lying down, but that failure has me crazy in the head already ...

I hope answers as soon as possible.

Thank you very much, greetings .....

Hmm, only thing you haven't tried that I can think of is check the MAF (air flow) sensor? May be dirty or faulty?

Hello Cyker, thanks for your answer ...

The MAF sensor you name is located in the same air filter box ...

I have tested this sensor and apparently it works, and I also cleaned it just in case, although in my case mine is like a piece of plastic ...

Any idea what might be wrong or dirty ?, the jerks continue ..

I wait for answers..

Thanks greetings

Good afternoon, to this day, with 462,000km and 25 years on the car right now, I still have the same problem. I have to say that when the car decelerates (releasing ALL the accelerator), it decelerates with small jerks that you perceive inside the car. If I accelerate the car from the engine (by hand) the jerks are not appreciated, the jerks are always with a gear engaged. Let's see if anyone can think of something or knows if someone else has had this problem and can help me please.

Thanks greetings.

Hello! Have solved that issue? Now I have the same. Year 2007, 320 000km. Not a single issue before that. Thanks.