You can totally build on an external drive, as long as the external drive is always available. You’ll want it to be formatted as NTFS, not as FAT32, though, so you’d need to re-format it after you unpack it. Doing this is inconvenient, though – one of the several reasons why people generally end up graduating to desktop workstations when they get deeper into UE game development.
If you already have an internal drive in a laptop, then you can buy a bigger drive, and clone all the old data to the new drive, and then extend the file system to have more space.
I don’t see why not.
I found a few links that go in that direction:
The later link has a bad SSL certificate, but it essentially recommends submitting /Game/Binaries/... and /Game/Plugins/*/Binaries/...