The Paladin's level 2 training in War surprises me a bit. I figured thematically he would be a more even balance of holy and war (3 each). But that's a minor issue, and I can understand why Arcane Wonders would want to avoid that for balance reasons.
However, I am worried about the Siren. She is the first mage to have 0 training in any primary school. That is a HUGE deal. There are exactly 8 existing cards in the Water school (not counting promos). Of those cards, only the [mwcard=MW1Q08]Elemental Wand[/mwcard] is higher than level one in Water, and two of the other cards ([mwcard=MWBG1J04]Raincloud[/mwcard] and [mwcard=DNI04]Renewing Rain[/mwcard]) are comprised of more than just the Water school. I can understand not giving her full Mind school access, but I really think she deserved training in the psychic sub-type.
So, what does she get to make up for this extremely limited card pool? Training in pirates and songs. Songs are a completely new sub-type of card (so this is a blind guess), but I can't imagine more than 2-3 songs per primary school. That leaves pirates. I can think of only a handful of non-creature pirate cards (including a pirate ship conjuration of some sort). Even if the Paladin vs Siren expansion consists of 75% Water, Song, and Pirate cards, I don't think the Siren will have an adequate card pool compared to other mages (especially the Paladin, who will have access to the majority of both the War and Holy schools). Every other mage in the game has in-school cards from multiple expansions to work with at this point. But even if the Siren does start out with a competitive card pool, how exactly are Arcane Wonders going to keep expanding it so that it stays competitive? Are they going to keep adding Water school cards just for the Siren with every future expansion after this?
Furthermore, the Siren controlling pirates doesn't make a whole lot of sense thematically (at least to me). In real-life myths Sirens were hated and feared by pirates and sailors, not seen as allies (that tends to happen when you are supposedly responsible for tons of shipwrecks). Pairing them up is kind of like giving the Druid training in Fire because forest fires sweep through tons of forests all the time in real life. Sure, there's a connection, but it's not a logical pairing. Grouping up pirates and the Siren also means we won't be getting a Pirate mage (War & Water) in the future, which I think is a missed opportunity.
On top of that, she possesses 9 channeling while two of her abilities require mana to use. The closest comparison to this is the Wizard, who also needs mana for his abilities but possesses 10 channeling. I get the feeling that the Siren is going to be mana-starved very frequently. Her third ability (regenerate 1 when in water) is decent but situational (Teleport might be a very good counter to her). Lastly, there's the issue of her health. She is tied for last place at 30 health with the Druid (a mage who realistically has 10 channeling so long as her chosen tree is alive).
So to summarize: the Siren will probably have a more limited natural card pool compared to other mages, leading to less efficient spellpoint usage. She has low channeling combined with mana-intensive abilities. And she is also one of the most frail mages to date. I want to love her, but at this point I remain thoroughly unconvinced.
Unless you've seen the whole set (which I haven't), there are a lot of assumptions here.
Training in Water provides access to some of the most commonly used utility spells, namely Dissolve/Crumble, Rust, Acid Ball and Surging Wave. Yes, the Druid also has access to those PLUS the entire Nature school, but it's also one of the main reasons Wizard just lost the ability to choose Water as his second school of training. And just like every other school, there's no reason Arcane Wonders can't include new Water spells (or Pirate or Song, for that matter) in future expansions. There is almost always a new good card for every existing mage in every expansion thereafter (except maybe the Academy expansions; they tend to be more focused on one mage type, although Tangleroot and Slumber are exceptions).
Next, there are about to be a TON of water-school spells. Have you been following the spoilers? This is the expansion where Water shows up in force. And some day we might see Frost damage type become a thing, which would also presumably fall within the Water school (although I guess it could be Nature, given how many Nature cards have the Frost -X trait)... so in general, i think the Siren will have plenty of spells she's trained in. But I think something you're missing is that NOT being trained in a school doesn't make it outlawed; it merely makes it cost the standard double. She's just as good as the Wizard (before or after yesterday) at casting out-of-school spells. You make it sound like she's paying triple for all non-Water spells. There's a HUGE difference. All Mind spells cost the standard double, which means all the level 1 Mind spells cost 2 sbp's, etc... so... fill your boots and include as many Psychic spells as you want!
As for Pirate training, I also found it unexpected, but it makes sense in that she is effectively mind-controlling them. Since you want her to have Psychic training, think of it like every Pirate has a free, permanent Mind Control on it. Done. These are just the Pirates that fell victim to her charms (and happen to be all the Pirates included in the game). And notice that the Pirates that have been announced (including promos) don't have the Aquatic subtype, so while she is trained in them, they don't tend to gain any bonuses (that we know of yet). The skeleton pirate looks much more at home in a Necromancer's book to me, as I see far more synergy there than in a Siren book... but then again, I haven't seen the whole expansion set yet, so I'll refrain from judging just yet.
Lastly, it's too early to be worried about her stats. I'd be shocked if she didn't have cards that boost them in some way. Druid has her treebond which is technically a mage ability but could have just been written on the Vine Tree spell card (but I get the impression the designers wanted to give a choice of which tree to play... although there seems to be an obviously best one at the moment), but i wouldn't be surprised if there is an Aquatic Terrain card, perhaps a "coral reef," that the Siren needs to protect that gives her +1 channeling and +X life, which automatically combos nicely with her built-in Regenerate and other abilities, and which is analogous to Treebond without using up a mage ability. Although maybe that would be too similar to the Druid (?).