.fai is propably the index file for the corresponding fasta file. You can just open it in any text editor you like. This file alone will be useless. Lot's of program that deal with fasta files use this additional file for faster access to specific sequences.
.gz is a compression format. In bioinformatic this is used to compress different file formats like
fasta and other. Doing this it saves space and programs that use this file as input can have random access (if the gzip version is blocked gzip, which is usually used in the field of bionformatic). Without knowing the exact filename no one can predict what the content of this file. If you can work with the shell just type
zless myfile.gz to have a look into the file.