Hello Hash4u, thank you for your interest.
Yes it Rev freely and absolutely fine in N and P and engine seems to be really perfect in condition. It also works well on R and works fine and very powerful on L even when it's cold. It's just D that doesn't work fine when the engine is cold.
I used Hyundai Oil for engine and for Gear it was something like ATF.
Yes the problem is there since I bought it and also the problem was there before changing oils.
How would I know if I'm using the correct oil? I'll update you soon on what oil I used.
Though, I did not changed the Transmission oil filter and I'm planning on changing it today and change the oil again Also I noticed the oil seems to be over filled.
I also noticed that the area below the Transmission Liver gets really hot after running the car for a while like if the transmission is getting hot. It becomes too hot that I have to pull my left leg away from transmission area. But when I check the Transmission Oil after drive it seems fine very little warm and not smelly. But I do feel some burning smell in the car while driving.
Engine temperatures seems to be fine and cool.