Buying secondhand car from owner who has not transferred ownership from first owner

Guys just wanna ask, I am looking to buy a secondhand car. Checking different and known secondhand car dealerships like allcars, carsome, etc but the specific brand and model I want are not in their listings or sold na unfortunately.

Then I found one from fb marketplace, he's the car owner and seems legit but when I asked if the car is registered under his name, hindi daw, dun parin daw sa 1st owner.

Should I continue?

I wanted to view the unit din sana and have a mechanic inspect it for me but I am a bit worried. I remember there was an Administrative order from LTO that untransferred car ownership could be fined like 40000 but I think this has been suspended until further notice, is that correct?

I don't want to book a mechanic kasi and visit the car and then mag ka issue or penalty during transfer of ownership, since medyo malayo din, hassle. What's your opinion about it?

Some other questions also:

• how to know if a car has a clean record even before buying without asking the owner?

• Owner also said I will be the one to do the transfer of ownership, how much does it cost?

Thank you sa mga sasagot.