Transacting with your own mint, will be free and also could be offline or in the same local network. No need to get out and swap between mints over LN.

You practically can create a fix amount of tokens and never get out into Bitcoin LN network, if you transact to each others.

Now, there's another story if you want to move funds from that mint into another or redeem (melt) some tokens into LN sats. That involve a real LN payment. It means fees, liquidity, channels, UTXOs etc.

ecash tokens are exactly like cash coins, only that are digital. That's all. Did you used those opendimes? Something like that, only that is easier to use and exchange.

No is not. Is the same as LN. The only new aspects is that it can be done without internet. You are playing around with IOUs.

The interesting aspect for end users and for you also, is that you can sell or give them these tokens as gift cards to be used to buy in your shop. You can say: "I will give you x discount if you use these tokens instead of paying me with other wallets". For both parties is better because is not necessary to use real LN liquidity.

Only if they want to spend those tokens in other places, where they do not use your mint. In that moment, they do not need to switch any other wallet, they could just pay with the same ecash wallet with your tokens, but it will involve a melt of them, transferring the sats into the other receiver LN channels.