How can I check progress of the email campaign that I've scheduled to send?

You can check the status of your scheduled email campaign using the Queue option found on the Content > Emails page as shown below:

Your Send Queue would look something like this:

You can Preview, Delete or even Pause your scheduled campaign from that same page.

If you pause a scheduled email campaign, it will remain paused even at/after the original scheduled time until it is unpaused. And once unpaused, it will go out immediately if the scheduled time has already passed.