If you include the ticket ID e.g. [ticket-id] in the commit's description, the commit will automatically be linked to that ticket. You can view the list of all associated commits with a ticket by clicking the 'Check-ins' menu item on the ticket's page. When an item is closed - the link appears struck-thru.

I dont automatically close tickets on commits - since our workflow is commits get reviewed before closing an item- but it is straight forward to write a small few line script to do this if thats your workflow.

Whatever you like. Workflow is a layer on top.