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I've searched the forums and faq and I haven't found an answer to this, so I apologize if this has been answered somewhere already.

First: I'm working under the assumption that by sacrificing a single spell you can grant multiple different bonuses, is that correct? For example: By sacrificing a level 3 spell, you get a +3 bonus which you can spend in several ways: to grant a +3 enhancement bonus; to grant a +2 enhancement bonus and the flaming ability; to grant the flaming, shocking and freezing abilities; etc.

Second: The rules text for Mage Bullets reads:

Many of these abilities are melee weapon-only special abilities (dancing, defending, spell storing, vicious and wounding). While some are easy to apply or work out (wounding and vicious, for example), others don't feel quite right (dancing or defending, especially dancing). So what's the deal here? Is this an error or is a Dancing Musket a thing? How would that work?

Hi, I've been searching for an answer for this for a while but I didn't find anything, so I guess I'll ask here. I'm building an alchemist but I'm not completely sure how to choose my initial formulae, the APG states that:
"An alchemist begins play with two 1st-level formulae of his choice, plus a number of additional forumlae (sic.) equal to his Intelligence modifier."

Does this mean that for those bonus formulae I could choose any formula of any level? The Core Rulebook, for Wizards, specifies explicitly that the additional spells have to be 1st-level spells, but that's not the case here.
I would assume that no, I can't choose to start with a 6th-level formula on my book (mostly because that would neither make sense nor be of any use), but I'd like to confirm that's how it's supposed to work.