In case my iPhone is turned off/out of battery, will I be receiving messages as iMessage or text message?
This may be helpful: from PC Pro blog: How iMessage works:
If you send a message to a fellow iMessage user who has their data switched off, the phone attempts to send it via the data channel at first, but if it can’t get through after five minutes or so, the message turns green and is sent via the traditional SMS channel instead. [emphasis mine]
See the article for more details.
This next might also be relevant if you have another iOS device you'd like to receive at instead, when your phone is off: gigaom - iOS 5: iMessage:
To ensure your Message is received on all your connected devices, you must have them sent to your Apple ID email address. In limited testing, if someone sent me a test message to just my phone number, I only got the text on my iPhone. However, if they sent the message to my me.com address (which is my Apple ID address), I got it on all devices. This is because Apple can’t associate your phone number (assigned by your carrier) with devices other than your iPhone.
Yes you will receive them. They will wait in Apple's servers. Though, it won't say "Delivered" on the sender's phone I think...