For the mapping of GO:
1. Find some list of species that have GO annotations
2. Find orthologs of each gene in your species to the genes in your reference species
3. The GO terms of the reference genes orthologous to a given gene in your species are your annotations for that gene
So if reference gene xyz has terms GO:123, GO:456, any gene orthologous to that in your species probably has those terms. Be sure to use best reciprocal blast hits, not just one-way blast. Here is a decent read on it: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2612752/. You can make your own tools to do this, or just use Blast2GO.
As for the TFBS mining, there are several approaches. The most basic of which is to compile a list of binding sites from phylogenetically close species, and perform a search using the collected PSFM. There are tons of websites that will have this data, just poke around for them. Shameless plug: check out CollecTF, a project I worked on. You can search -300 to +100bp of the TSS as a simplified model of a bacterial promoter.
As a note, be sure that your species actually has something orthologous to the TF whose sites you're looking for.
This would provide a looser but still interesting functional profile, if you know what regulators are acting on a given gene, you can infer what process that gene is part of. e.g. if a gene is regulated by LexA, it probably plays a role in stress response.
