how are lightning network payments instant and secure at the same time?
This is a very good question and I will give a quick summary of what is happening here. The longer version can be seen on my educational video on how to create payment channels starting at 33:41 (though I would recommend to watch from the beginning to review bitcoin and notation.) 


  My understanding being the multi sig wallet is a temporary address which will remain active until the LN channel is closed.


yes this is true! The key is a multi sig address which already prevents the attack setting to the shop which you discribed in the onchain bitcon setting without confirmations. If only you need a key for a double spend you can double spend. In the setting of the multisig you would need collaboration from the victim (shop) which would not do help you


  When it's closed a new transaction would be created distributing the funds to my wallet and the shop's wallet depending on where the funds were in the LN channel when the channel was closed


I think this is where you might not have the concept fully right. While it is true that the funds from the multisig wallet will be moved according to the distribution of funds to the two channel partners the initial transaction that spends those funds will be created even before the channel is opened by sending funds to the multisig from which this commitment transactions spends. 

All that being said. the funding transaction is not in the mempool as you guessed but in fact confirmed within the blockchain for the channel to be open and operational. So for an initial channel opening (unless using the somewhat special setting which allows turbochannels) one also has to wait for a couple of confirmations to use the channel safely. The setting with the shop also would not require you to have a direct channel with the shop. As soon as both you and the shop have channels connected to the network you should be able to pay the shop over a path of channels without the necessity to open another channel with the shop.