I don't think the end user needs to know anything about capacities or other technical details the same way a user doesn't need to know their internet speed.
The end user experience will be having a hot wallet in your computer/phone or online service like coinbase that will handle all the routing, channel setup, etc for you. Like when you use bittorrent you don't need to manually connect to peers, the bittorrent client handles that for you.
From what I understand--yes. They would need to "settle" their transfer on the blockchain and then open a new channel. The solution to this from what I've read is an IOU mechanism and a third party that has a channel with almost everyone. If the third party is rich then each channel is theoretically huge.
ALICE --(IOU to bob for 10k)---> CAROL --(IOU from alice for 10k)--> BOB
I'm a bit of a BTC novice here, so help me understand something: Does this not mean that on the LN there will necessarily be BTC that's essentially "floating" in the network, that hasn't settled on the Blockchain? What does this mean for liquidity and the integrity of the network in general?
Yep basically. BTC is tied up in channels and when you want to take it out of the lightning network you write a transaction to the actual block chain. Though with the way lightning routing works you can keep your money in the network for months or even years making hundreds of transactions. It's kind of like having a debit account (bitcoin lightning) and a savings account (bitcoin stored in cold storage) with your bank.
What happens to the engine trustless selling point of bitcoin when the only plausible scalability solutions entail reintroducing trusted third parties?
When a user opens a channel it has to lock up some BTC. That is called channel capacity because for payments to be routed through that channel (even other people's payments) that channel at least needs to have the same or more amount of BTC available. If you want to route a bigger payment you need to find a channel with more capacity.