Is it permissible for my brother to be a partner in a taxi for which I am paying installments, after he sold the first car in which he was my partner for a paltry sum and did not give me my full share?

Your brother is not permitted to give you less than half the value of the first car, because you are his partner in half of it. What he took in excess of his right is unlawful and he must return it, unless you willingly forgo it by delaying or gifting it to him. As for the other car, it is solely your property and its revenues belong to you alone. What your brother did in completing the bank procedures is recompensed by a fair wage (ujrat al-mithl), and it is not permissible for him to enter into a partnership with you without your consent. We advise you both to deal with each other with tolerance, cooperation, and overlooking (faults).