FaceTime failed and other iPhone problems?

Okay, so this has just been throughout the last week, I've been having a lot of problems with my iPhone regarding FaceTime and iMessage.
First of all, whenever I FaceTime ANYONE, even when it uses an email and not a phone number, I get a popup of the pic I attached. I don't know what it means because I'm using an email and there aren't any phone numbers linked to the contact. This started happening yesterday.
Also, I've been have so many iMessage problems! A couple days ago, my messages were sending, but they would show up in the screen for a couple seconds then disappear. The people I was sending the messages to could see the iMessages, but I couldn't.
Another problem I've been having for quite some time now is messages not showing up at all! They are sent to me and I won't receive them until I turn my phone off then back on again.
Please help! Is it just a but and Apple is fixing it? I just got my phone a few months ago and I didn't expect so many problems that completely defeat the purpose of having an iPhone!
ThanksFaceTime failed and other iPhone problems Added (1). I've already tried resetting the network, and it didn't do anything.

Post this question again in the correct category:

Consumer Electronics >> Cell/Mobile Phones & Pllans.

You're more 'likely' to get some answers there!