You will see Earth, Venus, Jupiter, Saturn. They are either bright enough, or come closer to Mars than Earth, that there are no complications/calculations necessary.
Uranus is just a naked eye object from Earth (magnitude 5.3-5.9). Its closest approach to Earth, when it is brightest is 17.2 au distant. Mars' orbit takes it closer by about 0.5 au, so you might have thought it would be more visible. But no - on average the visual extinction in the dusty atmosphere of Mars is around 0.5-1 astronomical magnitudes (see this relevant Astronomy SE answer) and this means the gain due to proximity (about 0.1 mag) is wiped out by the extinction. You would be very unlikely to see Uranus unless you had exceptional vision and knew where to look when Uranus was at its brightest.
Mercury is tricky. It is certainly bright enough to be seen from Mars, but would be sepated by a smaller angular distance from the Sun. The contrast between Sun and Mercury would be the same. I think on balance, it would be visible if you looked carefully, since Mercury can be seen from Earth when it is closer to the Sun than its maximum angular distance, though the Martian atmosphere might affect the glare from the Sun differently.
Your experiment with real data is fantastic! I applaud your curiosity, and investigation into the planets. Unfortunately, I don't think there's anything to your results (sorry!).
Astrophysics
The conventional wisdom used to be that planetary density would decrease with increasing distance away from a parent star, because that's what the disks around young stars look like [1] before they form planets. This idea completely fails in light of exoplanetary data which now includes thousands of planets in many hundreds of star systems. The end result is that planet formation is extremely complicated, and different types of planets tend to form in different places. In addition to that, there are numerous reasons to believe that planets move around a good amount after they've formed. So, observationally, there is no consistent relation between density and distance.
Statistics
If you try to plot enough relations, things will fit (e.g. Kepler's Shapes, and the Titus-Bode Law). The robustness of trends and correlations drop rapidly when, 1) data is arbitrary excluded (e.g. Mercury and Venus), 2) arbitrary split up your data, and 3) use arbitrary measures of goodness of fit (e.g. how close points look to a line on a certain plot). In fact, for robust statistical measurements, one needs to consider how many models were attempted to be fit, before considering how robust results seem.
[1] Even this is only approximately true... there were some more complicated reasons based on lifetimes of different substances in the disks, but that's not too important here.
Best Answer
To build on Martin Beckett's answer (especially because I am not sure how familiar you are with physics);
Currently we believe Stars form when objects known as Molecular Clouds (which are as one might guess, clouds of molecules in space, mostly comprised of hydrogen) collapse. It is important to note that these clouds are not 'static', they have some kind of motion, including some kind of 'average rotation', which is to say that overall the cloud is rotating (usually fairly slowly).
As was mentioned in Martin Beckett's answer, angular momentum is conserved; the typical example to give is to imagine a spinning figure skater, as she brings her arms in close to her body, she spins faster. If you don't believe this and have access to an office chair, it is easy to convince yourself (and possibly injure yourself too...). This holds true for the molecular cloud as well. As it collapses in on itself, it starts rotating faster and faster, forming a disc. The bulk of this coalesces into a big ball of hydrogen at the centre, which will eventually form a star. The matter in the disc slowly starts to clump together more and more to form the planets (it's a little more complicated than this, but if you're interested it's an easy topic to read up on). Similarly to how the overall cloud starts spinning faster and faster, the matter that forms these planets was spinning and maintains its spin as it clumps together into planets.
The previous post has covered your other questions.