Walaikum asalam
I hope you are well.
1) It depends on where the car is registered. If it is a Punjab registered vehicle and you are the seller then obviously you'll put up an ad here on pakwheels or olx or Facebook marketplace and prospective buyers will contact you. You'll then arrange for them to inspect the car and state an asking price. Usually there is margin (you'll have to study the market to figure out the value of your car). Answer any queries regarding the condition of the vehicle and describe existing problems or repair work that's been done. I have noticed that sellers who give maintenance history are appreciated a lot by buyers. Once the deal is done you'll take some token money (usually 5k to 10k) from the buyer which basically means you'll not sell the car to anyone else during the stipulated time in which the buyer has promised to pay the full price agreed by you and him. It is better to get the payment in form of bank draft or pay order.
You'll need a sale deed and a buyer's receipt (easily available on internet, generic forms). For Punjab registered vehicles the buyer will initiate a transfer of ownership application on epay app and pay the challan fee against the PSID that's generated by the app. This obviously will be done after the full payment has been received by you and you have handed over the vehicle along with file and smart card /registration book to the buyer. The file must contain the original invoice of the vehicle. Once the challan fee is paid against the PSID then you will be provided by the application number by buyer and you will give biometric against that from nearest NADRA sahulat center. And that's just about it.
2) For new car the process is simple. You will go to the dealership of the car you are buying and make the payment via bank draft or pay order. After that you'll get a sale's invoice that's needed for registration of new car. After receiving the vehcile, you will then visit the excise department for registration of the vehicle. Most dealerships do provide registration services so you can ask about that. You can also reserve a specific registration number on the mtmis website and take part in the auction. If nobody else bids on it then probably it takes 2000 Rs for reservation of a specific number. You'll pay the registration fee (depends on the engine category) and also some money for the smart card and number plates ( it's all included in the same bill).
Generally that's the procedure. I didn't catch the third topic since you haven't written about it.