The core doesn't reach all the way down but I'm not sure how much that matters. I guess it depends how quickly you drink it - if there's still water in the bottom by the time the core has melted then that water is going to have warmed up again. As long as the core is still cool, if you slosh the water about a bit before you drink it it'll still have the same effect.
I haven't had any leaks with mine, but I can see how you might. It has a screw top then a little 'flip top' catch that you drink out of. That flip top locks in kind of two stages - you flip it over to close it then you have to press it down until it clicks. I'd imagine if you forgot to do that second bit it could come open in a bag or something.
Basically, I can see how people would get those things but I haven't had them. I do stuff in the gym or walking though, so I can't comment whether it's a good water bottle for runners.
TBH, I've never seen a product on Amazon that
somebody hasn't posted complaints about. Unless they're all negative... well it's only a fiver after all.
Jon