First, I'd like to point out there's already a topic with Homemade Classes, if you look around and it would be nice if all homebrewed classes ended-up in the same place.
Anyway, I find the idea very interesting, but as it is now, it looks a bit too strong. Just a quick comparison with the Freelancer should be enough to show that the Alchemist is invariably stronger. Also, the class you've rolled so far looks much more like a fighter class or at least mixed fighter class, than a Novel.
Now let's "dissect" the Alchemist class step by step:
Alchemy is a form of ritualistic magic with strong scientific-chemical ties, actually allowing to perform some forms of "magic" for anyone who has studied enough to perform the complex rituals. Under this aspect, if you think about it, it's very similar to Summoning in Anima. Summoning can be performed by those without the gift, all you have to do is study the complex rituals and learn how to perform them.
For Alchemy I'd suggest a similar Zeon-Based Gift-Free system. I'd make Alchemy rituals work as Summoning Onces (with time penalties applied, since only very strong alchemists can make circles in few seconds...always remember that the alchemists featured in Full Metal Alchemist are the top-notch alchemists of that world!). Hence increasing difficulties in the check should allow the Alchemist (who has to spend the Zeon as well), to perform a certain "spell". Spells accessible to Alchemy should be selected from around the paths and the number of rituals known to an Alchemist should be somewhat limited. Again, using Magic Level (Alchemy Level in this case) could be a very good solution, since it's a limited resource that allows an Alchemist to work no better and no worse than an average mage of the same level. For rituals I'd Roll Science+d100 (Open Rolls allowed as well as Fumbles). Difficulty of the check might be
Spell LevelXCasting LevelX2.
This formula has a difficulty range going from 4 (Level2 Spell cast on Base Level) to 640 (Level80 Spell cast on Arcane Level).
Of course Alchemy to work need something "equivalent" to be put at stake. Of course High and Divine magic are out of reach for mortals even when they use Alchemy. Also, very high Occult levels should also help in Alchemic rituals. 1/10Occult (round down at multiples of 5) should be added to the check, meaning an Occult Master would have a nice +20 bonus to rituals. Also, Intelligence Limit for casting spell effects should apply to Alchemy as well. After all increasing Intelligence is good anyway for this class, since it raises both Science and Occult and grants more Alchemy Level, hence new tricks.
Finally there's the problem about projecting Spells (since some of the spells in the Alchemist's arsenal should be attack/spiritual/defense). I'd use Magic Projection just because it's easy. No matter how you summon a fire bolt or a earth spike, the ability to direct it on target should be developed in a similar way by mages and alchemists alike.
Now, with this Alchemy system in mind...let's work to the class.
Two things are important for an Alchemist: Zeon and Science. Also a PURE Alchemyst shouldn't be a fighter. Again, Alchemists in FMA are often sort of multi-class character and are such high levels that have had plenty of time (or adventures) to refine themselves both as warriors and alchemy. An Alchemist should be a pure Mystic Archetype Class.
For simplicity, let's take the Wizard scaffold.
Magic Accumulation cost should be raised to 60 as is for a Summoner, since it's only actually required for Regeneration (and the Alchemist can always buy Regeneration Multiples instead of Accumulation Multiples for half the cost). Also Zeon/Level should be the same as for a summoner, so +50Zeon/Level instead of the Wizard's +100.
As for the secondaries, appy reduced cost to Science instead of Magic Appraisal and add +10Science and Occult per Level (no bonus to Magic Appraisal/Level).
Like this the class gets -50Zeon/Level and pays more for Magic Accumulation (well...since it has to buy only Magic Regeneration, we might say that it actually pays it LESS). Also on average this class has +5/Level on Secondary Abilities.
Some of you might argue that this class is "weaker" than Wizard BUT they should note an important detail: although Alchemy is ritual based, so suffering penalties for quick-casting AND requires material components of some kind to be performed, an Alchemist at creation has +2CP compared to a Wizard, since no Gift is required and this very much balances the things since 2CP are a HUGE amount of CPs in this game.
Now, since I understand you like the idea of "fighting alchemists" as is in FMA...we need a Warrior Alchemist class (from mixed Mystic-Fighter Archetype).
Same process here.
Take the Warlock
MA Multiple goes to 60DP
Add Reduced Cost Science.
+5Science/Level and +5Occult/Level (no bonus to Magic Appraisal/Level).
That's how I'd work-out Alchemy and Alchemists in Anima System, of course but in your games you're free to make them work as you like.
I don't have time right now to scroll all spell list and choose those spells that would be fitting for alchemists. It would also be very interesting making a skill tree based on Alchemy Level just like the Arcana Sephira for Wizards, but working with Alchemy as an alternative way of spending Alchemy Level instead of just buying new spells.
Hope these ideas were helpful! Your idea was very interesting to me and I believe I'm going to work it out somehow in my own games!