Notice first that by clicking "Block" you can view how the transaction actually looks in the bitcoin network. Here's an example of one of those "0 fees" (Asset Issuance of "1020 JODI"):
https://blockchain.info/tx/8e382205e147d42f3092ab885c35f049b84edaeb9ee9921315395eb0780fac1e
So indeed the right column in your table is the normal bitcoin transaction fee (miners fee). Now every bitcoin transaction needs to have an output. Since those CP operations in your table do not have any recipient, you need still to put something in that field. It seems that most people are using here (like in my example) a clever trick to send just small amount of BTC to back to oneself: they are put into "escrow" (one out of oneself). I believe .0001086 BTC is the smallest amount above the dust level. "BTCAmount" in your table is just the actual amount sent to another address. For some reason not all CP transactions are using the escrow trick but instead they are sending the .0001086 BTC to another address (CP protocol is indifferent in what you do in the destination field in the operations like the ones in your table), but it is not any type of fee.

This is also the place (I think) Friction has planned the new fee I talked earlier. Instead of having these "self escrows" or whatever, it would be required that an amout of IXCs needs to be transfered to a certain address (this is the "Mastercoin way"), i.e. "the Foundation fee". IMO, that's a good idea, but I wish he would discuss the fee amounts etc here instead of just putting whatever pleases him. IMO, the fees should be rather small (to encourage the use of IXC CP) and also rather simple (to prevent complications in the long term). My preferered way would be to have the amount send to Foundation to be exactly the same amount as paid to miners regardless of the CP action. This would be very easy to check from the implementation point of view (so easy that it could be easily implemented as native if needed) needing no adjustments in the future, and IMO it is also fair ("half to miners, half to the Foundation"). Also from the users's perspective, it would not be too expensive (double of making a normal IXC transfer).