Noteworthy points if you're going for hard sci-fi: if you're not handwaving artificial gravity, most of the ship will be zero-g and will be unsuitable for long term use (on the space station, astronauts lose approximate 1.5% of bone and muscle density per month without multiple hours of specialized exercise each month to simulate gravity). The most plausible explanation is going to be rotational gravity, where a part of the ship rotates to simulate gravity with centrifugal force - the most common designs being an outer "ring" around the shuttle that continuously rotates, connected to an inner gear that connects to the main body of the shuttle.
Hydroponics (plants) can be grown in zero-G, specifically lettuce, potatoes, cabbage, onions, bok choy, and wheat. Fruit is a much harder sell than vegetables and likely has to be included in the centrifuge because of the increased vascular system necessary in the base plant.
Likewise, astronauts in space are likely to be rotated on a regular basis through hydroponics, both for psychological benefits and to ensure cross-training on the most vital part of the ship. There's likely a greenery officer that is either constantly out of stasis (however that's implemented, or even if it is) to make sure no plant contracts blight, or a certified rotation, just in case.
Open water is generally a terrible idea, but if there's a storage tank where water is diverted after being purified, it probably doubles as a makeshift bathtub or pool simply because no one would be able to resist it. Just make sure everyone purifies it again afterwards. Immersion in water has tremendous health benefits, not least because swimming is a full-body activity that works all the muscles neglected by zero-g.
Population density is going to be high in the domicile area just because you want people sleeping in regular-g if possible, out on the rotator ring, rather than having them sleep in 0-g and then having to go out to rotator for several hours to counterbalance the effects. That said, the ship proper is likely to be much more empty, so people can take long moonwalks down empty parts of the ship without interruption.
Of course most of my speculation here is reliant on actual space physics. If you handwave gravity, then you have no reason not to have those things, though any parkland / water is going to be highly isolated; water and soil strata is fertile ground for microorganisms to flourish, and bacteria / virus cultures in space behave very, very strangely.
Yes, that crazy bunch who designed a capsule to fit a V2 and were going to send a test pilot suborbital in 1949 if the government had let them.
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