Am I allowed to use gates with a data width of 2 bits and more to simplify the circuit, or must I implement it at the single bit level?
Yes, you are allowed to use logic gates with multi-bit inputs/outputs, as long as the fan-in is at most 2 (where applicable).
If you do use multi-bit gates, please make sure that you properly understand how multi-bit gates are constructed from single-bit gates. You must be able to build such multi-bit gates yourself, if and when required.