The pronoun se is not being used as a reflexive pronoun here. This is an impersonal construction. Impersonal se is used to make general observations without assigning actions (or obligations, or capabilities, as in this case) to any specific subject. You'll probably learn about this in time.
There's no grammatical equivalent to the impersonal se in English; the closest is the pronoun one, which is employed, like se, in the third person singular (One must do what is right). In English you generally use you for general observations (see what I just did there?), since one may sound stilted, or you use they for unspecified agents.
Se puede means something like "One can" or "It is allowed". So ¿Se puede? means "Is it allowed?" or "May I?" or even "Is it OK?". When to use this impersonal construction and when the personal one is a matter of context.
The impersonal construction distances the speaker from the hearer. This might be considered respectful or rude according to the circumstances, the tone, and you exactly you want (to be given permission, to receive some object, to get something done).
If you're talking directly to someone and asking for permission to do something, it is usually OK to use something like ¿Puedo? (or more indirectly: ¿Podría?). For example:
¿Puedo entrar un momento? ("Can I go in for a moment?")
¿Podría dejar esto aquí? ("May I leave this here?")
If you instead ask ¿Se puede? it may sound more like you're simply asking if there is a rule. It's OK, though, if you want to ask tactfully about something in general, even though it's actually for you. For example:
¿Se pueden dejar las cosas aquí? ("Can one leave one's things here?")
The impersonal might be rude in some cases if you use it to demand something. It is the same as in English when you say e.g. "Can anyone get a good drink around here?" or the like. This has a lot to do with your tone, though. You can make a polite indirect demand using the impersonal, for example:
¿Se puede encender el aire acondicionado? ("Could the A/C be turned on?").
¿Se podría hacer un espacio allá? ("Could some room be made over there?")
As an aside, you don't say ¿puedo tener un vaso de agua? in Spanish. Tener is not used for drinking or eating. You need to say something like:
¿Me puedes/podrías dar un vaso de agua (por favor)?
("Can/could you give me a glass of water (please)?")
¿Me das/darías un vaso de agua?
(*Will/would you give me a glass of water?")
You could also ask:
¿Puedo tomar un vaso de agua?
("Can I drink a glass of water?")
but that suggests you're asking for permission to drink, rather than for the water itself.