1. If you are driving your car now, come here immediately and give me a ride home.
( Is this one correct? In this sentence, the driver is in the middle of driving his car. Is that right?)
2. If you are driving your car after work, give me a ride home.
( In this sentence, the driver is not driving his car. He will drive his car later after work. Later the person wants to ride the driver's car, doesn't he?)
Your interpretations of these sentences are correct. You could omit 'your car' each time since that is implied in the word 'driving.'
I'd also add 'please' after each comma.
1. The sentence "If you are driving your car now, come here immediately and give me a ride home" implies that the driver is currently in the process of driving their car. However, since the sentence uses the word "now," it suggests that the person making the request wants the driver to interrupt their current task of driving and immediately come to the person's location to give them a ride home. It is important to note that interrupting the driver while they are operating a vehicle can be dangerous and should be avoided.
2. In the sentence "If you are driving your car after work, give me a ride home," it means that the person making the request knows that the driver will be driving their car after work. The person is requesting a ride home at that specific time when the driver is planning to drive their car. It implies that the driver is not currently driving at the moment the request is being made, but will be driving their car later after work.