In game, with no interaction with anything, you will be logged out to the lobby in 5 minutes. Clicking anywhere or interacting with anything will rest this timer. In the lobby, you have 1 hour of no interaction I.E (personal messaging friends, talking in friend or clan chat, switching worlds, or simply clicking anywhere) until you are completely logged out.
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You don't really "play on Facebook"; you just associate a Facebook account with RuneScape. After that, if you are already logged in into Facebook, you can select RuneScape from there and don't need to login again.
The only way to play the original version of runescape is to have an active account when "runescape 1" was still running. An account is deemed active if the player has logged in within the last 6 months.
Never timed it, but 1-2 minutes is a safe guess.
Go underneath Lumbridge and get a mouse or a spider to attack you. All they hit is 0 so you don't have to worry about dying New answer: After the recent updates, you get logged out after 5 minutes even in combat if you don't perform any actions. Taping down a key doesn't work either. I would recommend using something to constantly click.
Maybe your monitor isn't connected properly, or if that's not the case, you are playing Runescape with Too-High detail.