Can FASTA files have nucleotide and protein sequences within them; or must they only have 1 type?
While there's nothing stopping anyone from doing that with the FASTA format (after all, it's just a text file with '>' defining header lines), I don't know of any software that would support such a file structure. At best, it would interpret the nucleotide sequences as protein sequences (A/C/G/T are all valid 1-letter protein codes).

A better question to ask would be "Does ultra-cool-bioinformatics-tool X support combined nucleotide and protein sequences in the same FASTA file?" In which case the answer would most likely be, "No."