If you have to use someones elses payment channel to get through, how is it decided how much fee are you paying the channel owner?
The channel owner determines that fee. If you don't like their fee, then you can choose to use a different channel to route your payment through.
If you can't spend small amounts, then how will it solve micro-transactions, or having unusable wallets with amounts smaller than fees?
It isn't really that you spend small amounts, but rather that you can send and receive many small amounts without paying a lot in fees.