He has sponsored magic (we're calling it Phoenix Fire) that's sort of a modified version of Seelie Magic. This type of sponsored magic gives him fire, air, and spirit spells, and biomancy at the speed of evocation. It has "themes" like balance, growth, renewal, and rebirth.
3 different elements given from one Sponsored Magic is probably too many for only -4 refresh. If you look, most sponsored magics grant one, maybe at most 2 if you broadly interpret them.
1. Does biomancy break the law of magic about transforming if you're only repairing or renewing the natural processes of a body? Such as closing a bullet wound or, maybe, regrowing a severed limb at the extreme? This isn't biomancy that transforms a person into a fish or anything. It's very similar to the Reiki/Healing Touch thing Elaine did in the books, I think. Did that break the laws of magic?
Elaine basically was "helping" bloodflow and manipulating chakra points, pushing a little extra with her magic, not really doing much "healing" as it were in terms of direct tissue manipulation with magic.
Technically that's a grey area, and a zealous Warden would
technically be in his rights to perform a head-ectomy, if he has jurisdiction over the PC under the Accords. I generally interpret that Law to require the magic to be "against their will or when you screw up." As long as you don't screw up, and you don't transform them against their will (even healing, if they don't want it, would count here), then you're fine. Of course, the more you do this, the more you're inclined to go to that solution first for your problems...so the GM should be compelling one of your PC's aspects (and you should self-compel) to push in that direction whether you've broken a Law yet or not.
2. How do focus items work for sponsored magic? Using the fire magic part of Seelie Magic as the example, should it be a wand with a +1 offensive control Seelie Magic? OR +1 offensive control fire?
This is really a question for the table and your specific GM. Some people allow catch-all foci, some require them to be split between evocation/thaumaturgy...but then some thaumaturgy is done at evocation speed, so how is that calculated? It's not mentioned in the book at all, and there's no exactly right answer.
I tend to prefer to require separate foci for evocation and thaumaturgy; if using thaum-as-evocation then the evocation foci take precedence. Your setup is a little wonky because of the multiple-elements. It might be more appropriate/easier to combine characteristics of air, spirit, and fire into a new, single "Phoenix Fire" element.