Sorry if I misunderstand you but it seems you don't understand the concept of LN (maybe you do but then I don't understand your post). The money doesn't move 'on chain' from Bob to alice. Both deposit 0.1 BTC into their channel, THAT is an on-chain transaction.
Correct and it locks an amount for Bob and Alice on the chain (I assume that will be free, lock manager)
When everything is settled the money needs to move from the channel
It was never in the channel as such, just locked on the main block-chain to ensure each party
had money to cover settlement so what really went between Bob and Alice was IOU's backed by insurance if you like
Do both pay $30 for opening the channel (when they both wire money into the channel) ?
No they are free to open, real BTC on the BC never moved and the $30 miners cannot be split because
money on the BTC block is always sent and the sender pays the costs to send just like sending a letter
Think about it this way. We walk into a casino and both deposit $100 each with the cashier and she gives us both
100 cheap plastic tokens each so we pick a table and play flick the coin but it's only a two player game (Private ledger) and I end up with 190 tokens
and your only left with 10 so then we return to the cashier and the nice lady give me $190 cash and you $10 (Our original
money back) and she then looks at you and says it's custom here for the loser to pick up the settlement charge for us lending
you the table and you now owe the nice lady $30 please (Miners transaction fees)