Relayers
A relayer submits your signed operation and pays the gas. In return it receives the fee you signed, in vault shares. Anyone can relay; the app can also submit from your connected wallet.
Network fee
The vault publishes a suggested fee, updated at most hourly, from maxOpCostWei and the price average. It is a suggestion; you sign the fee you accept.
Avoiding linkage
Paying gas from your main wallet for a stealth address would link the two. Signed operations avoid that.