Am I entitled to claim car expenses that I paid for two years after leaving the company, knowing that the company owner gifted it to me and informed me that its expenses would be covered by the company?

If the car expenses are part of the company's obligations and you paid them, you can claim them if, at the time of payment, you intended to claim them back from the company. However, if you intended it as a donation, you are not entitled to claim them. And if you made the payment without a specific intention, you are also not entitled to claim them back.