Ah, well. The game was updated a bit ago, so Lonely Cave is a new place. The thing is, only YOU can see it. You will only ever be the only one there. If you look around, there are two black spaces in in the wall, two portals. There is also one in the water and one on top of the cave. If you go through there, it will take you to other places where there will be people.
Chat- You can chat by typing in the chat box on the left. If you click the button that says "Local" when you first sign in, you can change which chat you're in. General chat is for... well, anything in general. Local chat can only be heard based on how far away you are from others. whisper is sent directly to another player that only they can hear. Group and party chats are from invites.
Friend and group requests- Most of the time you will end up whispering people to join groups. When this happens, the three paw prints down at the bottom will show a little number 1 where you can accept the request. You'll then be able to hear the group in group chat. Same works for friends, though some people accept random friend requests and some do not.
Where I suggest you start- Try heading to Fluorite Plains. This would be the portal in the water. It says "Cape of Distant Worlds" Go through that and there should be another portal at one end taking you to the Plains. WarninG: Around this time you most likely will get bad tokens. You just have to keep trying and you will get in eventually :] The plains is the most heavily populated area and you will most likely find some groups there you will like.