Is it possible to install pfSense from a USB stick, or will I need an external CD drive?
You can run from it if you're using the embedded version, but if you're looking to do a full install, it's not possible with the stable version, you need a CD drive. There are USB stick equivalents of the iso for 2.0 at snapshots.pfsense.org.
pfSense can be written directly to the USB stick, and you can boot and run it from that. pfSense doesn't have anything in the official docs about installing from a USB stick, which means it's likely going to be difficult to do.