Learn Dutch: Ik heb alleen water.

It can mean both! In this sentence, because it describes what you have, it translates to "only". If you were to say Ik ben alleen, it would mean "I am alone." Context usually makes it clear which one is meant.

Could I use maar instead of alleen here?

Yes! You will often hear Dutch speakers say Ik heb maar water or even Ik heb alleen maar water to mean the exact same thing: "I only have water."

Why is the verb heb and not heeft?

The verb is hebben (to have). Because the subject of the sentence is Ik (I), you must use the matching "I" form of the verb, which is heb. You would use heeft if the subject was "he", "she", or "it".

Why isn't there an article like het before water?

Just like in English, we don't use words for "the" or "a" when talking about general, uncountable things like liquids. "I have water" translates perfectly to Ik heb water without needing an extra word.