Is it permissible to buy a car under the aforementioned circumstances, and is Takaful insurance on it permissible, bearing in mind that insurance is mandatory in the country?

Insurance is of two types: Takaful (cooperative) which is permissible, and commercial which is forbidden. If the regulations of an insurance company fulfill the conditions of Takaful insurance, then insurance with them is permissible. Otherwise, it is not permissible to insure with them optionally. In the absence of a Shariah-compliant alternative and if the insurance is obligatory, then it is permissible to limit it to third-party insurance, and the sin falls upon the one who enforces it.