Sierra255 has it right! One of the reasons for WiFi taking over is so that you don't use your data plan, which saves you money on metered data. On my Droid Razr Maxx, I would have the 3g/4g indicator on all the time, but it would turn blue when connected, and it would turn white when I was on WiFi.
As for the SMS/MMS problem. Have you tried a third party text program such as Handcent or GoSMS to see if the problem is with default application, or the phone/network. If it happens in the third party app, then I would give Verizon a call.
Finally for daydream: on my Nexus 7, daydream only kicks in when i have the tablet in the dock. I'm not sure if the s4 is supposed to behave the same way, but it could be the reason why you're having trouble...