Translation:There is no water in the glass.
I think this should be accepted. For the Chinese to specifically be glass rather than any kind of cup I think it should be 玻璃杯. That said I think glass is probably an acceptable as a translation of 杯子 given the tendancy of the term "glass" to be used as a synonym for cup in some cases in English (i.e. It's sometimes used to refer to cups not made of glass).
Chinese is highly contextual, and I think one could indicate multiple glasses from context (as the quantity is not explicitly stated). That said, you could also probably something like 这些杯子里没有水。(these glasses have no water in them) if you want to be explicit about which glasses and their plurality
'There is no' +noun is grammatically correct, to use 'there is not' you would also need to add 'any' before the noun. Check https://dictionary.cambridge.org/grammar/british-grammar/no-or-not if you don't trust me.. ;)
"no water" is correct. "No" in this context is a negative article.
Grammatically, "not" may be acceptable, but idiomatically it is incorrect.
Correct: There is no one in the house There are no fish in the ocean.
Incorrect: There is not one in the house. There is not fish in the ocean.