The record for lightning is $1m recently https://www.tradingview.com/news/financemagnates:db022676a09...

I imagine the seconds to pay won't be true - if they are exchanging emails and inspecting boats it's going to be an hours to days long process.

Transaction fees are based on the complexity of the inputs/outputs, not the value transacted. You are literally paying for the minimum amount of data necessary to prove you own the funded sending-address, paying to write those hashes and amounts into the blockchain. The institution handling this offchaing lightning branch can implement fees in whatever structure you agree to transact, including percentage based.

Lightning is just an off-chain out-branch, which will eventually be re-integrated onto the main blockchain (based on its original funding/terms). The benefit of this is that single entities can branch off the main blockchain, which is limited in its total blocksize/capacity.

The only limits are those by the handling lightning institution. This differs from bitcoin's main public blockchain, which rewards/creates approximately six blocks /hour, each with a limit of just a couple megabytes.