My suggestion would be to leave the car in Salerno and use the ferry instead.
Salerno - Amalfi ferry: you can visit Amalfi and Atrani since they are basically one next to the other; wander their streets; spend time on the beach; visit the Amalfi Duomo, Paper Museum .etc;
Amalfi - Positano ferry: take the ferry to Positano; wander through Positano; spend time on the beach; see the newly opened Villa Romana;
Positano - Salerno ferry: take the ferry from Positano back to Salerno;
This way you would have visited 3 Amalfi Coast towns as well as admire the entire coast from the sea since Positano is the last town in your direction and Vietri sul Mare is the first from Salerno.
If you are leaving the area the next day, and depending on your destination, you could do the Amalfi Drive with your car just so you could experience the coast from another perspective. Best if you leave early as to avoid the traffic.
I was wondering that can I find car parking lots easly in towns ?
You will have a hard time finding parking. Also, traffic is very congested.
Do you recommend to use the public transport instead driving car in May ?
Yes, absolutely. Ferry is the 1st option, then SITA bus.
Can I go to Sorrento and come back to Salerno at the same day ?
I don’t think this is doable. It’s too much crammed into one day. Better leave Sorrento for another day.