So after continuous efforts and guidance by @Hassan1991 my Honda Accord CM5 2005 issues of Gear Jerks, Pick up, and Oxygen sensor check engine light has been resolved this is what we have done.
Diagnosis:
we got to know that the head assembly of my CM5 has been changed by the previous owner to RBB-3 which comes in high-performance K24a engines. The original engine of CM5 is k24a4 and its block code is RAA and comes with a simple Automatic Transmission. it's a non-performance engine while k24a with RBB block is a high-performance engine.
1) Replaced the gear. Installed a triptronic that comes with CL9/CL7.
2) Replaced the Throttle from a simple to an electronic one.
3) Installed an electronic paddle.
4) Changed ECU of the Car to 7Y RBB.
5) Replaced wiring from CM5 to CL9.
6) Replaced oxygen sensor s1.
7) Replaced Gear Lever and meter to support triptronic gear.
Everything was available in Bilal Gunj except the oxygen sensor. We tried multiple oxygen sensors but were unable to find the right one. All of them were throwing P0134 errors. We got the oxygen sensor from an electrician called Heera and his shop is near Bhatta Chowk.
All of this cost me around 230K PKR.
We got all of this stuff from Khalid Brothers in Bilal Gunj.
Mechanic and Electrician both were provided by him.
The name of the electrician is Adnan.
The name of the mechanic is Amir.
@Hassan1991 has been so helpful throughout this journey. I am so grateful for his help. My car is trouble-free just because of him. It wasn't possible without Hassan.
I have driven the car for more than 150 km so far. The pick and gear conversion of the car is extremely smooth. The fuel average has improved to 8.5-9 and earlier it was hardly 4-4.5 km/liter in the city.
Thanks to everyone on forums and especially @Hassan1991 for guidance and help.