You can get the session ID via the session helper... session()->getId(). I don't believe you can check the time left of the session before expiry. I'd suggest checking this post on StackOverflow for a workaround if you want to track session time left.
Looking at the docs, you'll see the Database session driver tracks last_activity, using the SO link above and this knowledge you could implement a last_activity on the users table while using the cookies session driver.
If you want to redirect after a session has expired, you need to implement a poll/ajax call that calls every x seconds or minutes that pings an endpoint and checks if the user is logged in via say auth()->check() if false, then on your frontend you can redirect them or show them a login modal.