Would love to be able to instant message (remember AOL days—is this dating me?) team members. Intuitively I am looking for it on the bottom right, where I can see which team members are active and then be able to send them a direct message. Would also be cool to @ mention a certain task or project within the chat.
Hi @Abbey_Rodriguez, welcome to the forum!
You can send private messages using the orange + button at the top right of the screen or from your Inbox.
In the ‘To’ field you can @[team name] to easily send to all team members instead of typing all their names out. And in the message body you can @ a project name or task 
Check out Send Messages to Other Asana Users • Asana Product Guide