Mitsubishi Galant 2001 LS V6, newly occurring Transmission Problem.

I have ongoing problems with my cooling system. Rusted radiator and No heat. There were leaks at multiple places. Which caused me to add at least a gallon of antifreeze every week. I get all the leaks fixed, one by one as they appeared.

Leak 1:
Radiator replacement was the first thing in this stop leak process. Because the first leak that we track down was from the coolant reservoir overflow. Block in the radiator and a broken rim of the radiator that comes in to contact with the radiator cap were the culprits to cause fluid to flush in the reservoir bottle overflow. During radiator replacement the following happened. As soon as the mechanic replaced the radiator (with a new one), I asked him to check the coolant flow in the heater core in and out hoses, to check the heat. Now, to check the flow in these - in and out hoses of the heater core, mechanic turned on the car and as soon as he turned it on, I've realized that that guy forgot to join the transmission hoses going into the radiator. That caused a loss of about 2 quarts of transmission fluid. Which he replaced with Valvoline brand fluid. This incidence took place 4 days back. The radiator replacement stopped the overflow of the reservoir bottle.

Leak 2:
Now, after the radiator replacement and coolant fill up, I drove my car about 8 miles to get back to home. No problems were seen so far. No leak, but heater was still not woking. The day after, I again drove 9 miles to an fro my house. But, when I reached back to home and stopped my car (not the engine), there was a heavy smoke coming from below the hood. I couldn't find any visible leak of coolant, but I was sure it was coolant because there was running water over the ground due to rain and I saw green coolant mixing with it while the engine was still very very hot and smoke was making clouds. The other day I went to a local mechanic within half a mile from my house and he found a broken hose that was causing coolant leak. He replaced it and there was not leak after he it (I checked this by running the engine idle for like 2 hours but not driving the car).

Leak 3:
The Fourth day from the radiator replacement i.e. today morning I drove 3 mile to and fro my house. When I came back again I saw a loads and loads of smoke coming from below the hood. I turned of the engine and open the hood. I saw a leak from one of the gasket from the metal part at the other end of the top radiator hose. I again went to the same local mechanic and he changed the gasket.

So that was my story of 3 leaks that I found one after another upon rectifying the previous.

Now there is no leak. Buttttttttttt, today night, When I took out my car from parking and went to eat out, I noticed some weird behavior in the transmission process and moving forward the car. Following are the strange behaviors that caused me to start suspecting a problem in the transmission.

1. After I turned on my car, I put it on 'R' and went about a foot back from the parked place (Because my car was parallel parked). Then I put the shift on 'D' to move forward. Usually, I don't have to paddle gas to move my car a bit. Like in this case of coming out of the parking position. But, this time I had to make a conscious effort to move my card forward. I though that was probably due to snow underneath my car.

2. I noticed same kind of conscious effort when I took a stop near a drive thru restaurant window. Usually, when I lift my foot from the break, cars starts moving slowly. But, this time it wasn't. It felt like it was still on 'P'. So, I had to make a conscious effort to move it forward.

3. After going a mile from the above stop (I was driving normally), There was a sudden and automatic jerky changes in the revs of the car. That moved form around 1 to 3.5 k all of a sudden without me doing but not really accelerating the car, car was actually becoming slow. There was also jerks in the movement of the car, too.

4. After few seconds of the above, all of the sudden car was not responding at all to my push on the gas paddle. It was like car being in neutral. So, I put it on 'D3' from 'D' and it moved normally but there was a little heavy feeling on the movement of the car (as same as the one you usually notice when u put car on 'D3'). So, it felt like a normal behavior.

5. After driving about 10 feet on 'D3' I again put my car on D and then it went smoothly for around 2 miles. After that I again felt those jerks and then had to drive the car in 'D3' for 15-20 feet to park at Shoprite (where we were heading).

6. After coming out of the Shop-rite in like 30 mins. I drove my car for 3-4 miles to reach home and did not notice any weirdness during this 3-4 miles.

With all of the above description, can any body please help me suggesting what to do now. What could be the problem and where to start from to know and get rid of the problem?