Should toggle buttons show current state?
Yes behind the scenes it is a state transition but to the user, there is an action. Whereas Shuffle/Straight Play is an option and it's best to show the current state (and possibly have only one icon and change button to show that the option is enabled/disabled).
Should buttons have tooltips?
If you're introducing the button as a new element & needs to draw users' attention you should use tooltip. It will help users to learn. *If the button explains itself clearly, we should not use tooltip.