I suppose it should be the cost of the hat (0.0001 btc) + the mining fees, correct?
I'm not familiar with lightning network, so I can't answer if this is correct. But there's a fee when you close your channel (you don't have to) and there was an user said about "commit fee".
What if I wanted to purchase from a different merchant this time; merchant B? Do I have to open a new channel?
You don't have to open a new channel if you can route your existing channel to Merchant B's channel and this is almost free.
Reference:
No, you only pay a fee when opening and closing a payment channel. Once the channel is open, you can transact freely (i.e. as many times as you want) with the other person in the channel at no cost. If you want to transact with someone outside of the channel but there is some route to them through LN channels, then you can use your same channel to pay that other person by routing a payment through other channels. This routing of payments will either be extremely cheap or have no cost, depending on whether node operators in the route charge a fee for being routed through.
If you are just going to make a single transaction with someone and you don't plan on using them to route payments to other people, then you should not create a channel for that. Just make a normal Bitcoin transaction.
Since I don't have any open channels in Electrum at the moment, I experimented a bit with my LND node. I have recently spent 0.00591658 BTC on a channel opening transaction. Right now, I can spend 578 053 satoshi through that channel and its reserve is 5916 satoshi. 578 053 + 5916 = 583 969 satoshi, so it turned out that I was also missing some coins. I found an additional parameter called "Commit Fee". This value tells how much money you are going to pay for the closing transaction fee if either you or the other party broadcasts the current commitment transaction (a transaction which records balances in the channel). In my case, it was equal to 13 605 satoshi. 578 053 + 13 605 = 591 658 satoshi. Great!