Some people say that certain sweeteners affect their weight loss, but that's definitely not proven, and LT and CD both have aspartame so I doubt it's true. Just see how it goes for you.
Probably - you'll have to see how it works for you. Wouldn't overdo it as anecdotally, fizzy things have made some people hungrier, but yeah, see how it goes.
Personally, I actually find that having a can of diet cola curbs my appetite, it takes the edge of it so I normally reach for a can during the weekend as this is when I find the diet the hardest.