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If your back link profile is good it's just coincidental that your traffic drop, your IP address change, and Penguin2 all happened on the same day, then wait it out--obviously you're doing something well to have all those back links. If your link profile is on the low quality side, it's probably time to start cleaning house and doing the things penguin victims have to do. Here's a little more info on the May 22nd penguin update.

There is no relationship between AdWords and organic.  I've spent over $30MM in AdWords, and have several relationships with dedicated AdWords reps, and have never been able to get anything special from the organic team  (I've tried several times, with 0 success).  I could not even get the organic side to expedite a reconsideration request.

They might have some signals related to IP address but in my opinion that should not have a large weight. Your site might have a new load speed, and this is a signal for rankings as far as I know. You can use Alexa toolbar to see your domain's speed average, but it was better if you knew your previous speed, I think Google Webmaster Tools also shows you page load times, check if that increased when host changed. I hope this helps.