Re: group text downloading
Wow. I've never had that particular problem, but I have experienced equally frustrating situations. I'd say keep your 4G on whenever you're anticipating a group message, and don't mess with your data unless you're willing to accept the consequences! I don't think it's an issue exclusive to the S4 or TMO, it seems from my experience that SMS is a million types of screwed up in itself as a thing. I constantly get duplicate messages from people, messages out of order, without using groups or screwing with my data connections.
So, to summarize, SMS is cool and convenient but doesn't work a well as it should for anyone, and screwing with your data to save power can do all sorts of things outside of your Messaging app. My battery seems to last me a single day at school with WiFi, GPS, Bluetooth, and NFC on all day, and I'm a heavy user, so maybe you should reevaluate your usage rather than cut out 4G data...