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... and pay 5-10 $ fee per transaction? I doubt it.

Right now the median fee on lightning is $0.000226047.

Next question: where can I get Lightning banknotes for offline payments?

You say that like any argentinian would walk around with money or any valuable after he abolishes the police.

You are aware people have been carried valuable items with them long before the invention of police?

Lightning is not a solution, as it requires buying into a channel and not getting your coins until the channel closes.

You can always use level 2s for small transcations.

And potentially wait many multiples of 10 minutes if the mempool is full, making it potentially useless.

Lightning doesn't require waiting. Block time is not relevant unless you're sending a very large amount of money.

Sounds like a fun time waiting for transaction to process in the shop