Ok, thank you so much!So here is what i know.
Yes every person who buys a car needs to register it in his name. So if you are not keeping the car, dont register it, when you sell it the buyer will.
The cost is the same, it will only differ when another year passes. Newer cars registrations are more expensive than older ones, also it depends on the horsepower of your vehicle
Now for your other question, when you sell your car, you (or someone legally assigned by you) have to go down to the car registry thing (the location depends on where you live) with the new buyer to transfer the ownership of the car to his name, all this can be done in around 1h30mins or so.
So you transfer the ownership, he registers the car in his name, gets his new plates and you take yours. All in around 2 hours.