The P<>K bridge charges user fees on originating Asset Hub, but it pays relayer rewards from AssetHubs' sovereign accounts on sibling BridgeHub parachains. These relayer rewards are a large part of the bridge's "operating costs". For initial deployment, AssetHub's sovereign accounts on BridgeHubs should be pre-funded by treasury. An initial 10100 DOT and 2030 KSM is proposed to be split among the relevant system chain sovereign accounts to provide initial bootstrap runway to the bridge. This will only be an initial seed. As the bridge operates, it should cover operation costs (relayer fees) from the user fees paid on Asset Hub, and any unspent user fees ("bridge profits") are going to the treasury anyway, so in the longer term these funds are practically paid back (plus profits). Exact system chain addresses being funded and amounts for each can be found here: https://github.com/polkadot-fellows/runtimes/issues/238
Yes, of course we need to add fuel.