Right now, there's only one-on-one action with the party members.

There are the random encounters on those maps that drop the samples when you have the quest.

You can check the walkthrough for this, just press Ctrl+F to open the search bar, and type in the names of the events you're looking for.

That is the normal starting area where you can start the game or just see the gallery for the events. As for why you can't move, try to use W, A, S and D. The mouse doesn't work, unless you remove "Cae_NoTouchMove.js" from the folder Small On Top\www\js\plugins. You can't use the mouse to move because it caused bugs to appear and you would go out of bounds.

There's a third party member that needs to join you before you can grab that item from the stone. Just progress in the story a bit more, and you'll eventually meet him.