Is it a proper translation to use the English "she is drinking water" with this sentence? Or is there a present imperfect tense I don't know about yet in Irish?
This is the equivalent of the present simple tense in English. You'll see the present continuous later on; it will take the form of tá+verbal noun.
Is the "sí" optional? As "I eat an apple." was previously translated to "Ithim úll." and not "Ithim mé úll.", would "Ólann uisce." also be acceptable here? (Of course, you wouldn't know which (grammatical) gender the drinker had, but that could be inferred from context.)
Edit: I read in some other comments I read that "ithim" already contains "mé", i.e. that the "m" stems from a contraction. A confirmation would still be nice, but this would imply that you probably can't just leave out the pronoun.
"Ithim" means "I eat" all on its own, so it doesn't need a pronoun. "Ithim mé" would mean "I eat me".
You use "itheann" with a pronoun for all other persons. The exception is "we", where you have a choice: you can write either "Itheann muid" or the shorter form "Ithimid", whichever you prefer.