I am not up to par on my healing knowledge... but first aid and the heal spell seems redundant. To the best of my limited knowledge once you use heal you can't
use first aid. But you probably already knew that and you are seeing something I am missing. Otherwise looks good.
Being good at both is still nice, though, because as long as you use 'em in the right order, you can REALLY patch someone up.
Pretty sure you can only use one type of healing on any set of injuries.
However as was recently pointed out to me, in SR4 you can use First Aid to heal Drain-inflicted damage (which Magical healing cannot do).
As for the rest of the PC, I've played several Mystic adepts and also think you're spread too thin (even for a 350BP campaign).
Having a banishing of 5 seems nice, however the drain in doing so will be intense, and basically take you out of the fight (3 Charisma is not going to be of help here), and as mentioned before, not much Edge as backup.
I'd recommend the following:
A) Drop Banishing 5 and get the whole Conjuring group @1 (-20 points, plus 10 points = 10 points net gain). You'll get access to summon some minor spitis which is always a helpful utility for any awakened to have (Watcher spirits are always nice!), and you can always raise the requires skills later if the campaign progresses
B) Get the 'Animal Husbandry' skill group @1 (Running Wild sourcebook, p.34). Your PC is obviously very much flavoured to be around animals, and these skills will mean that you actually have some abilities to assist (and stacks with the Adept
Animal Empathy power)
C) Drop some of the the language skills knowledge skills. For a 350BP character, each BP is precious, and to utilise so many (for what I'm sure are GREAT background reasons) is going to hurt.
With Int+Logic =7, you get 14 Knowledge points for free, plus your native language. You've spent another 14 BP on top of that. I really recommend you just choose a few key knowledge skills, and if you really want, take the '
Bilingual' quality (5BP, Runners' Companion' p.96) to get a second native language listed (no skill points required).
If you're desperate for more knowledge skills, grab a few cheap KnowSoft programs on Magical Phenomenon etc. They're legal, cheap and will save you BP

So, if you've spent all 14 points, plus 5BP on a second language, you have a net gain of 9 BP.
D) Items: It seems odd for a low power PC to use money (and karma) on a couple of low rating Foci. Recommend dropping these and spending the money (and bonding BP/Karma) somewhere else
E) Spells... too many for a Mystic Adept. With 1 initiative pass and not a lot of Drain capability you will have neither the time nor inclination to sling this much mojo.
- The Fix spell sounds nice, but in play is incredibly hard to use for a beginning character. You need 5 successes to fix anything technological, and with Spellcasting/Magic rolling 8-9 dice (11 with Edge) you're likely better off giving it to someone with some tech skills to fix it. Drop this spell (net gain 3 BP)
- Control animal/Calm Pack. Again, Stretching yourself too thin, and doubling up. Choose one of these and learn the other at a later stage during the game (net gain, 3BP)
- Levitate/Heal These are excellent utility spells, so keeping these makes sense.
- Manabolt: Change this to a
Stun bolt. The drain is lower, and it gives you a
non-lethal way to deal with opposition (and it's just as effective as a Manabolt against spirits/paranormals!

). If you really want to kill something, stun bolt them twice so that the Stun damage overflows into physical....
- Offensive Mana Barrier. I don't know why you're using this? It's an intensely draining spell, and may keep out minor spirits/dual-natured creatures, but otherwise do very little (apart from pretty much knock you out from drain). Recommend dropping this spell (net gain 3BP)
- Increase Reflexes: Grab this spell. Sustain it if you can, or pick up a R3+ focus during game with cash/acquisitions. This will give you extra initiative passes, which will double/triple/quadruple your productivity if caught in a fight. This should be a mandatory spell (net loss, 3BP)
So, with the recommendations above (if you take them), you'll have 13BP more to spend (enough for another attribute point and another spell), but will still be able to rock the house with your utility and animal powers.
Of course, feel free to ignore any/all fo the above. They're just suggestions and at the end of the day, you have to play the PC
YOU want.
Have fun! 