Praise be to Allah.
It is not permissible to celebrate birthdays or other invented occasions or festivals, whether they are religious or secular, because of what that involves of introducing innovations and imitating the disbelievers. See the answer to question no. 26804.
The basic principle is that a person should not accept any gifts that are given to him on these occasions, because accepting them is approving of the celebration and helping to perpetuate it. But if the giver insists, and the person fears that a refusal will lead to negative consequences, then he should accept his gift, and explain to him that he has not accepted it because of the innovated celebration; rather he has accepted it because of ties of kinship, love and so on. See the answer to question no. 146449.
There is nothing wrong with making use of gifts that were given on these occasions, and were accepted based on a belief that it is permissible to celebrate and exchange gifts on these occasions, or out of ignorance, or in order to ward off negative consequences, as mentioned above.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: Just as Islam erases what came before it (of sins), repentance also erases what came before it, especially the repentance of one who may be excused, who just learned about the text or just understood it after having been unable to hear the text or understand it. This is very obvious.
The same applies with regard to contracts and acquisitions that he had not heard were prohibited, because of ignorance of which the cause was justifiable, or because of a misinterpretation.
So if he entered into a transaction or contract believing it to be permissible on the basis of a misinterpretation, such as riba (usury), gambling, the price of alcohol, an invalid marriage or anything else, then he came to know the truth and repented, or he referred the matter to us for judgement, or he asked us for a fatwa, then he may keep whatever he acquired through these transactions and contracts, and the marriage for which there was a reason to regard it as invalid may be confirmed, such as if he got married without the presence of the woman’s guardian, or without witnesses, because he believed that that was permissible, or he married a fifth wife during the ‘iddah of the fourth, or he entered into a tahleel marriage [a short-term marriage solely for the purpose of making it permissible for a thrice-divorced woman to go back to her first husband] concerning which there was a difference of scholarly opinion, and so on. Even if he later finds out that the marriage was invalid, it is to be confirmed and approved.
The point here is that if it becomes certain that the contract was haraam on the basis of a definitive text – such as becoming certain that one who was a disbeliever had become a Muslim in a true sense – then we affirm the marriage contract that he did in the past, and what he acquired on the basis of an invalid contract, provided that what made it invalid is not still there…
But there is a difference of opinion concerning that in our madhhab [i.e., the madhhab of Imam Ahmad] and others.
The invalid argument of those who disagree with our view: they regard this issue as something that is forbidden, and doing something that is forbidden will lead to mischief and evil, and will lead to regarding the cases of all Muslims involved in such issues as being the same, without differentiating between one who based his action on a misinterpretation of the text and others.
End quote from Majmoo‘ al-Fataawa (22/12).
And he said (29/412): The same applies to any contract that the Muslim believed to be valid, based on a wrong view, whether that was his only view or he was following the view of a scholar, such as riba-based transactions that are regarded as permissible by those who think that it is permissible to use trickery in order to make such transactions permissible. End quote.
Based on that, there is nothing wrong with your friend using that car or with taking a ride in that car.
For more information, please see the answer to question no. 226504.
And Allah knows best