2 Questions...

The players can't see the art library. Is that a DM only thing? When I or the player tries to drag and drop equipment/weapons from the compendium to their character sheet, it doesn't seem to allow that. Am I missing something?

Yes, the art library is a DM only thing. Compendium drag and drop is dependent on the sheet you're using, on whether the sheet is "popped out" in its own window or not, and whether you're selecting the correct entry (I can't tell you how many times I've dragged the proficiency over instead of a weapon).

An art library is tied to each individual account. This means the Joe's library is tied to his account while Joan's library is tied to hers. They can not be seen by others. If someone created a game and have tokens to be used in it by someone else, they need to create a token page (blank map page filled with the tokens) so the co-gm can have access to those tokens for that specific game. The compendium is what Dakota says but remember that an art library and compendium are two different things.

It may not be as simple as stated. I was in a game last week and tried to drag a spell onto my character sheet and failed. I had the character sheet as a separate window on a separate monitor to the tabletop. Afterwards i discovered that if you drag to the table top you get a message on the character sheet (on the other monitor) recognizing the drag and when you release on the table top it does update the sheet. If you are focused on the character sheet and try to drag directly there you can miss the "opportunity" to drop on the table top.

The available functionality is reduced when a character sheet or handout is popped out.