No, lightning network does not keep your money, but its a channel based on the bitcoin blockchain.
Yes they are banks, they charge transaction fees and interest on the BTC used by the bank to finance the ledger
and you admit this yourself in the link you provided.
Time value of funds locked in channels: This is hard to calculate. With proper fee adjustment, I believe the LN can work well with each intra-hub channel having capacity equal to a tenth of an average persons salary. This would mean that, Alice can pay Bob a total of 5 months salary before saturating all routes between them (if she wants more, she can always pay on-chain). Note that this would not saturate the intermediate channels between Alice and anyone else, though it might saturate Alices own channels. If the average salary is $1000, this means a total of ($1000*4M*4K/10) = $1.6T locked. Since Bitcoin is non-inflationary, the time-value of money is low; we will use a generous estimate of 5%/yr for the time value and cost of security. This gives a cost of $80B per year, much more significant than setting up channels.
One cent per transaction you say because the running costs of the hubs are so cheap so lets revers engineer maths
here and account for how miners were able to charge $55 per transaction two months ago if no one is out to make
profits that you ignore in the document.
$55 per 250 bytes, well lets call it $200 per K and this put the price of a gigabyte needed for a movie at about a billion squid !
I tend to get my information from the official white paper
https://lightning.network/lightning-network-paper.pdf or the
current network map
https://lnmainnet.gaben.win/ of lightning and each fork is inflationary, doubles the money supply and Lightning
really turns the bitcoin block-chain into a central banks for the hubs and this is required for anyone to trust the hubs.
off-block single point of failure banking hubs is not the solution and we are being feed problem-reaction-solution here.