Is there a flight mode feature where i can still browse the web? Basically, I just want to appear to other people as I'm offline/my battery is dead.

How can I do this?

I'm not talking about blocking contacts, but the effect would be the same as to block all of them for a given period of time I guess.
You can press the Airplane mode and then enable only WiFi. So your mobile data connection to your carrier is off (can't receive calls/SMS) but your online and have a internet connection.

But if you want to appear offline for certain online-apps like WhatsApp or Facebook you have to manually close these apps or log out or something...