Why don't I get a notification that I have a mms waiting? Iphone?

When your cellular data is turned off, you will have NO CLUE that someone is trying to send you and MMS (such as a picture). The phone won't even notify you; which means you will NEVER even know they sent it to you unless they tell you.

I want to turn my cellular data off to save battery and to avoid unnecessary data usage. On my Samsung Galaxy Ace2x I was able to turn my data off, and when I received a picture it would tell me to turn my cellular data on to download the picture; but with the iPhone it does not. So is there any way to make the iPhone do this, or must I keep my data on 24/7?

I don't think iPhones have the same ability as your old phone yet, but what I would do is let your friends know that if they want to send you a photo, they should let you know before they actually send it so you can turn it on for a few minutes to receive the photo.