It does not exist, however, there is a really great game actually called RuneScape, you could try that instead.
The best place to look up a private server would be Runelocus.
There is a few that you may be able to find on Runelocus.
Go www.moparscape.org ( moparscape's original site) and find out.
You find all the quests in the quest list, click on the quest tab.
You may what to find out about that elsewhere, not many people on this site tend to answer questions like that.
What do you mean by find a server. Like a private server?
you only get them from quests or random events
The top floor of Draynor Manor.
You find out by doing the in search of the myreque and the return of the myreque quests.
These worlds are for runescape players to gather together to complete quests together. Some players might want to have some company when doing quests, these worlds (although not proven :p) might increase the chances that you find someone doing the same quest as you. Sone quests in Runescape require partners to finish the quests eg. Shield of Arrav, these worlds might make it more simpler to find a partner.
In the server list, look for a server with a lock next to it.
Google.