It's supposed to be a trick that works - only filling the bottle about 2/3 full so there's an air gap. Something to do with the pressure and helping the water come out better. Bottles can stop working. I tap the spout every day to check water is coming out. As Cypher says you need to change the water every day. Maybe every 2 days is ok in colder weather.
I tend to have two bottles in the cage just in case one stops working. As for seeing if they've drunk any, they drink such a small amount usually each day that you don't really notice the amount being less in the bottle. You change the water so there is fresh rather than it ever running out
Even when our last hammy was older and drinking a lot more I didn't notice the level go down much.
You could try a bowl as well as suggested above, but some hamsters won't drink out of a bowl. You also have to be careful where you put it as they could fall in it and getting very wet can make them unwell. Plus it needs to be in a place where it can't be polluted by substrate, food, poops etc falling in it.
Personally I prefer to just have two water bottles, then if one stops working the other one will - and check/change them every day or two. You don't need huge water bottles either - mouse sized ones are fine
I find them easier to attach as well.