What is the ruling on using gifts presented during unlawful holidays, such as Christmas, and what is the ruling on riding in a car that was purchased for this occasion?

Celebrating birthdays or any other innovated (bid'ah) festivals is not legislated in Islam. The default is not to accept gifts given on these occasions, as doing so implies an endorsement of the celebration and an aid to it. However, if refusing the gift would lead to a greater harm, then it may be accepted, while clarifying that it is not accepted due to the innovated celebration. There is no harm in utilizing gifts that were accepted due to a belief in the permissibility of the celebration, or out of ignorance, or to avert harm. This is because repentance erases what came before it, and a person is upheld on what they have received from contracts they believed to be permissible due to ignorance or interpretation, as mentioned by Sheikh al-Islam Ibn Taymiyyah.