Generally, we say おなかがすいている、おなかがすいた、おなかがへった, etc for "I'm hungry!". if you want to use the kanji 飢, it's 飢えている[うえている] though I wouldn't use it in everyday conversation. However, there are cases that you see this kanji on the movie, anime or manga, it means "be hungry for", "be lacking ~ ", not only for food or drink, but also other things. I hope this was helpful.

Yeah, mostly they speak お腹がすいた. Also I've met お腹が減った in the same meaning. When you are thirsty , you can say 喉がかわく.

One option that I hear a lot is: おなかがすいた！