I wouldn't worry too much about those spots, they are most likely due to excessive use of fertilizers. Just stop using them.
About those suckers... is your fig tree grafted or not? Suckers can be used for propagation (through ground layering), but if the tree is grafted you'll get something completely unlike the scion.
However I suggest you just remove them because they are not just draining the tree of strength that could go into growing the main trunk and the figs themselves. You can always propagate the tree at a later date through cuttings.
