"iMessage" is a message transport. The app is "Messages". The document from Apple specifically says "SMS": it does not mention either Messages or iMessage. While it's possible that Apple leaves iMessages unencrypted on the device, it would be surprising given how much trouble they go through to protect then in transit. So while this document doesn't explicitly say iMessages are safe, it also doesn't say they're vulnerable.

It's big enough to carry everything you've mentioned, but no bigger than necessary. It comfortably distributes the weight when fully loaded, and is unbelievably durable. I've used mine on a daily basis for four years, including several cross-country and international trips, and it still looks new. Worth every penny. Highly recommended.