So, looking at the recent Jericho Reach preview, I read the list of the Harpy's biomorphs, and I realize that I have no idea how many of those weapons it could fire in a round. I don't know if it can fire multiple weapons, if it would have penalties for doing so, etc.. Similarly, with say a Tyranid Warrior, I ASSUME it wouldn't have need of Ready actions since its weapons are connected, but honestly I don't remember such a thing being spelled out.

I would doubt it especially since they're natural weapons. How many it can fire in a round depends on how many Actions the attack takes (half/full) and relevant talents just like anything else.

From my reading the Harpy would get one attack per round. It doesn't have traits like multiple arms, swift attack, or the like. I would treat every one of those powers as some kind of attack action. As Kshatriya says, your attacks per round are governed by talents and traits, so I'd assume the creature would get one attack; using its arms, its cannon, or one of the special powers.

As for having to ready them, from my reading of each of the powers and the weapons, they're all continually readied. All the spikes and things are controlled by muscle contractions, the scream is a scream, scything talons is just swinging your arms. Unless the weapon seemed to be out of the creature's hands for some reason, I'd not ever require them to draw the weapon.

As a HR, if my player's kill team was already too deadly versus Tyranids (or just have extra high dodges or the like), I would consider adding multiple attacks, and allow her to fire her firearm and use a special Harpy power in the same turn, but I do feel that I would be customizing the creature by doing that.