Little staircase symbol with an R on top: means that you are using paid data: http://www.galaxys5manual.com/android-icons-meaning/
The staircase icon shows the strength of the wide LAN.
Turn off: http://www.gadgetdaily.xyz/quick-tip-how-to-turn-off-data-roaming-on-android/
On 5.1, the "Mobile data" is also present on the default settings bar. It clearly explains that internet connection is gone unless you have Wifi.