Sounds like you're referring to image clip. Hold the s pen close to the screen and click the button on the s pen and select image clip, it'll let you trace around a pic and cut out the selected area.
Probably an app, something is keeping the phone awake even while the screen is off. Just checked my battery stats and my phone is pretty much only awake while my screen is on
Here's mine with 3 hours screen on time
It's hard to say, but as litlprince2 stated the screen is the biggest battery drain. Also web browsing over WiFi will be different then browsing over LTE, signal strength also makes a difference