У меня already implies possession. Есть would be optional in this case, though still permissible.

У means like by/at. So the scentence can literally mean "By me is water and coffee" or "I have water and coffee" if it's obvious.

The Tips & notes say that the possession is the subject and therefore in indicative.

No, вода is actually the subject of the sentence, hence it is in the nominative case.

When you click on a lesson in your language tree, a tips & notes secton is at the bottom. (Only for some lessons.) It's indeed easy to miss if you have a small screen.

Я is always "I", not "me". When you say, "It's me" in English, you are using incorrect grammar. Correct English would be, "It is I", but we just don't say it that way because it sounds pretentious.

@Tony Shark, SashaMsf

Я = "I" or, sometimes, "me" it's me! Малдер, это я!)

У = at, by: у окна - by the window; у ворот - at the gate.

So "У меня вода и яблоки" literally means

By me (there are) water and apples.

Я means I and У is like a particle or preposition