Is there a way such as the jailbroken iPhone app BiteSMS that allows sending and replying to texts from anywhere on the phone?
If you like the native texting app and just want the added popup... I recommend "SMS Popup" from the Play Store, its free.
I thought FB Messenger did support MMS now. Are you sure it doesn't?
It does. There's an attachment icon next to the text box that allows you to send it as an MMS message.