Querying the blockchain does not cost anything, just making changes to it. Otherwise, verifying transactions would be a recursive cost. I could be wrong though, but pretty sure since it's distributed reads are free, writes are where it costs.
Payment channels alone are only a good solution if you consider it acceptable to establish a payment channel with everyone you want to pay. So, in other words, it only makes sense for recurring payments to the same merchant, and you pay the blockchain fee once for each merchant you want to pay. Consequently, if you only pay once you pay the same fee as an on-chain transaction, and if you pay 1000 times you pay, in average, 1000th the blockchain fee per payment.