There isn’t a way to communicate with the FCC servers when you’re offline, so you can’t get data (including challenges) from FCC or send data (like solutions) to FCC. If you know that you’re going to be offline and wanting to work on stuff, you can grab the next few challenges (copy, screengrab, whatever) and work on them on your own computer. You’d have to spend some time learning how you set your computer up for offline development, but you can do it.
They’re listed under Take Home Projects in the last section of the curriculum.
Yup. It’s being looked at.