Can I slice a lemon or lime and float it in my water. Or is this considered eating fruiit.?

I see a few recipes with lemon or lime juice it but I am a bit confused about this.

Go ahead! The tiny amount of juice won't do any harm at all!

I miss Sprite- but I can't have artificial sweeteners so diet sprite is out. Would sodium free club soda with a little lime juice be horrible for me?

Not at all. Go for it!

I think lemons and limes are okay in small amounts (like a little juice in a recipe or a slice or squeeze in your water) because they have a lot of acid (which slows absorption of sugar into bloodstream), they don't have much sugar, and they add a LOT of flavor.