Well, if you're going to put lemon in your water, pre-slice it; I think that a paring knife would get confiscated at the gate.
I've never been stopped on any ride with my Brita bottle, and on some, I've even had it in my hand as I boarded. If you are concerned with that, I believe that the Culligan version is clear plastic.
The valve on a Brita bottle can be tricky, as it is a double-click valve. If you pull it up only halfway, water will come out, but only in a minor trickle--DS has to be watched to make sure that he doesn't put it in a backpack like that; because it will leak. At full open, it pulls out a bit more than a 1/4 inch, I would say. Also, you need to keep at least 3 inches of water in it to keep the flow going through the filter, because it draws the water in only through the end of the filter; less water than that, and it won't come out through the spout properly.