RAW: Inconclusive, ask your DM.
Let's take a look at your five requirements, but first let's keep this on hand:
You determine the environment within the demiplane when you manifest genesis, reflecting most any desire you can visualize. You determine factors such as atmosphere, water, temperature, and the general shape of the terrain. [...] You can’t create lingering psionic effects with this power; you have to add those separately, if desired. Similarly, you can’t create a demiplane out of esoteric material, such as silver or uranium; you’re limited to stone and dirt.
But what does this mean for your plane? Let's see:
A plane of pure water
Water is a mundane material, so it is possible. The "base" of your plane is not required to be dirt, and given the wording of you being able to determine the various attributes of the plane, "consist entirely out of water" is not directly ruled out by the rules. In fact, if you follow the rules for the demiplane traits in the Manual of the Planes (p.153), you can pick the Water-Dominant traint (p.12), which is described as a "mostly liquid plane". They can also have the no-gravity trait, creating an ball of water. The problem is the water escaping: see point 3 for a possible solution.
An "everfull" plane of water
More difficult. Consult the previous note on the Water-Dominant trait. Creating water is as far as I can tell not a "lingering psionic effect", despite the existence of the divine spell that does just that. Water could escape from a finite plane by sloshing over (see point 3), so there should be a way to keep the water in, or at least replenish the stuff that's taken. To solve the second problem you could chuck a Decanter of Endless Water in there. This can keep your demiplane filled with an endless amount of fresh water. If you DM is a dick though they'll tell you that over time a massive amount of water got stuck in a finite space you'll get a massive amount of water pressure in there, which will kill you once you step foot inside. And if the border (more on this below) gets ruptured you'll end up with the biggest "coke and Mentos" experiment in all of the multiverse.
A self-contained shape
Depends on how you read the rules. The rules mention that you create a "finite plane with limited access". But the rules for planar shapes mention a Self-Contained Shape, which folds in on itself. This is an addition to a finite-sized sized plane, so if your DM allows it, go ahead. Note that there is presedence for such things: Neth, The Plane that Lives (Manual of the Planes, p.154) is a plane normally 500 miles in diameter, but it normally has itself crumpled into a 25 mile ball. This creates exciting concepts for what a demiplane can be shaped like, but to keep it simple: What is the third dimension but a fold in the second?
Solving the water escaping problem can be done by making the plane in question have the whole "borders teleport one to the other end" rule described in the planar trait rules:
A spherical plane is an example of a self-contained, finite plane, but there can be cubes, toruses, and flat planes with magical edges that teleport the traveler to an opposite edge when he crosses them.
So now you have all the water in a spherical shape it can't escape from. Hurrah!
Gravity point in the center of the plane
If this is to solve your water escaping problem, this has been solved already. If not, it depends on your reading of you determining the factors of the plane and if this includes gravity. Also ntoe the rules for demiplane traits in the Manual of the Planes (p.153). If it works for you, give it heavy gravity and call it a day. If not, ask your DM.
As hot as can be (how hot can it be?)
Inconclusive. Temperature is something you can determine and no restraints are stated, so feel free to make it an octillion degrees and call it a day. Note that the rules are inconclusive on what happens regarding to heat bleeding out, and if you want to go into your plane you will want to prepare yourself. Ask your DM.
So in short, a summary of the answers:
- Depends on how and if you use the Demiplane Traits when using Genesis.
- As above. A Decanter of Endless Water can be used to achieve this goal if the Water-Dominant trait does not cover it.
- If allowed, use the self-contained shape from the traits list to teleport water around when it hits the border, keeping it from escaping.
- Depends on how you interprit the Demiplane Traits.
- Depends on how you interprit the Demiplane Traits.
So in short, Ask your DM.