See, "Having" the water would not only imply that you're 'drinking it' kinda way, but also that you have it or possess it. I have it with me. & I'm having it. That should be it.
I'd say not quite. "to have" is one of those exceptions. Because it is a so-called "stative" verb we can't use the present continuous to mean the same thing. Colloquially "having" is only really "eating" or "drinking" but not "to own".
"To see" is similar. "I am seeing her" is very awkward if it's supposed to mean "I see her." but it's an idiomatic way to say "I am dating her."
Does anyone know a trick to remembering the differences between the different forms of the words? It trips me up more than just knowing the words.
haben is harder because it doesn't follow a nice pattern.
ich habe = I have, du hast = you(singular) have, er/sie/es hat = he/she/it has, wir/Sie/sie haben = we/you(formal)/they have, ihr habt = you(plural) have
For general verbs that are nice and follow the rules (I'll use trinken as an example)
ich trinkE du trinkST er/sie/es trinkT wir/Sie/sie trinkEN ihr trinkT
The endings of the verbs will usually follow this pattern.
Hope this helps a bit!