Statements 1-4 are indeed correct1. According to Newtonian gravity, any two objects with non-zero masses impart a force on each other. Additionally, the force falls off as $r^{-2}$, so the force goes to zero only as $r\to\infty$. There's no finite cutoff. Now, there are obviously distances at which the force is too small to measure, and this is especially true for bodies with very little mass, such as atoms.
Statement 5 has me confused. You could say that an object at point $p$ a distance $r_p$ from another object with mass indeed feels the force of gravity from that other object, but I'm not sure how you would define it as "existing at both points at the same time". Gravity propagates at the speed of light (see this, this, and this), so gravitational effects aren't instantaneous, but both objects will indeed feel some sort of force.
Your final conclusion involves a bit more thinking. if an object is in a potential $\Phi(\mathbf{r})$, it will feel a force, given by the equation
$$F(\mathbf{r})=-\frac{d\Phi(\mathbf{r})}{dr}$$
where $\mathbf{r}$ is a position vector. If we can measure the force at a bunch of different $\mathbf{r}$, we can figure out $\Phi(\mathbf{r})$2. This, in turn, will allow us to figure out the density distribution of the matter causing the potential, by Gauss's law for gravity:
$$\nabla^2\Phi(\mathbf{r})=4\pi G\rho$$
In your case, it will tell us that the object being observed is being influenced by what is essentially a point mass. This approximation works because
- Atoms are extremely small and have very little mass.
- The atoms exerting the force are far away.
We're not going to get much good information about the structure of the cluster; it will seem like a point mass to us. The force between the cluster of atoms is going to be incredibly small, and this is what makes your idea not very feasible (see Has gravity ever been experimentally measured between two atoms?). Try plugging numbers into Newton's law of gravitation, taking the two masses to be the mass of a hydrogen atom and a small cluster of hydrogen atoms. Over any reasonable distances, the force of gravity between the two is going to be pretty much impossible to measure.
Another difficult arising here is that there are plenty of other effects - electromagnetic forces and other major sources of gravity, for starters - that will make any measurable force here insignificant. Using Poisson's equation is pointless (pun not intended); it would only tell us remotely useful information if used in an isolated system composed of only these atoms.
1 Statement 2 is actually a little wrong. The Sun is, largely, composed of plasma, which includes protons which have been stripped of their elections. But I think I'm being a little pedantic, as the mass of an electron is negligible compared to the mass of a proton.
If we can only measure the potential at one point, though, we don't know much about the global behavior of the density.
I think you meant that the surface on which we stand exerts equal and opposite force to balance gravitational pull, which we call as a normal force. If you have this understanding than you are correct about this statement, as it is important to distinguish that it is not the Earth that exerts a normal force, but the surface on which we stand. For example, if you stand on a table that is strong enough to hold you, it prevents you to fall further down as it is strong enough to provide the normal force that will balance your weight. Instead, if you try standing on water, you know what will happen! That's because the surface of the water is not hard enough to provide you with the necessary normal force.
So, here you need to understand that normal force always exists as a response to weight. If you place a 2 g weight on a table, the normal force will be less as compared to placing a 2 kg weight. As you increase the weight of an object placed (consider a bucket kept on the table which is getting filled with water) the normal force will also increase until a point where the surface is not strong enough to hold the object. Just think about this, can you harness any energy from a force whose mere existence is as a consequence of the existence of another force? You can't.
I hope I have understood your question, if not, please elaborate.
Best Answer
Whenever gravity exerts a force on an object, it is because there is another object in the vicinity. Both masses are required to create the force. If the mass of one object is double, the force is doubled. This happens for either object.
The formula for the gravitational force between the Earth (E) and the grasshopper (g) is $$F_{gE} = \frac{Gm_gm_E}{r^2}$$ where $F_{gE}$ is the force on the grasshopper due to the Earth, $m_g$ is the mass of the grasshopper, $m_E$ is the mass of the Earth, $r$S is the distance between the grasshopper and the center of the Earth, and $G$ is a constant.
Now, lets find the force on the Earth due to the grasshopper. We just switch the roles of $E$ and $g$: $$F_{Eg} = \frac{Gm_Em_g}{r^2}.$$ Because, $m_gm_E = m_Em_g$, we see that the force is the same. The grasshopper pulls on the Earth just as hard as the Earth pulls on the grasshopper.
This is one example of Newton's third law in action. If A exerts a force on B, the B exerts a force of equal magnitude on A.