No it is not. It would be reasonable for you to open a channel with your employer who also has a channel open with that coffee shop. Your employer would pay the transaction fees for you, and then you can pay the coffee shop. Later the employer would pay your through that channel.

No. As I said earlier, LN is not for spending from small outputs once but rather spending from large outputs in small amounts many times. The common use case scenario is that you put in (for example) 0.01 BTC into the channel with the coffee shop. Then over the course of months or years, you slowly pay the coffee shop 0.00001 BTC per coffee but without actually making any on-chain transactions and paying their transaction fees.