i think these are crematogaster ants, a.k.a. acrobatic ants (confirm by looking at the abdomen - if it's sort of heart shaped, i'm right). they are nesting in the decaying interior wood. not damaging to the living portion of the tree, somewhat damaging to the interior, physiologicaly dead wood (but, some evidence exists that any nests in decaying trees actually slows decay, by drying out the wood and reducing fungal vigor). I can't really tell much about the yellow fungal thing - where on the tree do you see it, does it have any height of it's own, or is it tight to the bark, etc. as for the whole tree (or, the trunk thereof...), it looks a bit like it may have some girdling roots, but more likely just trunk flare showing (looks like it is a grafted tree...). what you've done with the mulching and watering around the drip line (both inside and outside of same) is the most good you can do for the tree. trees take time to respond to changes, either positive or negative, so what happens this season will give you a better idea of how the tree is faring. mulberries are tough, so if any tree is going to absorb this damage with a minimal long term impacts, this is the one.
having said all that, given the decay of structural wood in the interior, which you can do nothing about, you are now in a position of managing the decline of the tree. even if the canopy returns to full health, the decay will continue at some rate, and will eventually result in a dangerous tree. that's probably years down the road, but coming.