Is there a Vellum account or server?
No account. Folder sync goes through your own sync service; device-to-device sync uses a small relay only to introduce devices, and it never sees your pages.
Two ways, both end-to-end encrypted with your passphrase: through a folder your computers already sync, or directly between devices you pair once by QR code. Nothing readable ever leaves a device.

Vellum writes an encrypted log of changes into a folder that iCloud Drive, Dropbox, OneDrive or Syncthing already syncs; your sync service carries the files to your other computers, where Vellum reads and merges them. It needs Chrome or Edge on a computer, which can read and write a folder you pick.
Phones and tablets sync directly with your other devices. Pair a device once by scanning a QR code (or typing a code); after that, the two exchange what the other is missing whenever both have Vellum open, over a direct, encrypted WebRTC connection. A computer that also syncs through a folder passes the phone’s changes on to the rest.
In Vellum, open Settings → Sync between devices.
Pick a folder that iCloud Drive, Dropbox, OneDrive or Syncthing already syncs, and a strong passphrase. Keep the passphrase safe: it can’t be recovered.
Under “Sync with another device”, choose “Show a pairing code” on one device; on the other, scan it or choose “Enter a code”, then enter the same passphrase.
Folder sync runs in the background on computers; paired devices sync whenever both have Vellum open.
No account. Folder sync goes through your own sync service; device-to-device sync uses a small relay only to introduce devices, and it never sees your pages.
Yes, by pairing the phone with another device. Folder sync itself needs Chrome or Edge on a computer.
The synced copy can’t be decrypted without it. Your pages on each device are unaffected; set up sync again with a new passphrase.