What should be the numbers in the fastSTRUCTURE file? The structure file for fastSTRUCTURE seem to be a table with rows and columns but the cells are all numbers, while my genotypes are simply bases. How could I know what I should insert there?
Numbers, usually in the form of 0/1/2, is a common way many formats represent bases.
For example, if a SNPs has bases which are A/T, then these are encoded as 0/1, with the reference allele/base taking the 0 and the alternate allele/base taking 1.
However, if you read the documentation, it says:

Specifically, rows in the data file correspond to samples, with two
rows per sample (note that only diploids are handled by this
software), and columns correspond to SNPs. The first 6 columns of the
file will be ignored; these typically would include IDs, metadata,
etc. This software only handles bi-allelic loci. The two alleles at
each locus can be encoded as desired; however, missing data should be
encoded as `-9'.

So you should be able to use your base letters here and it will work OK as long as the columns and rows are formatted correctly.