If I understand your description correctly, you have a maximal load area of ~38 ft². If so, 4x4s are more than sufficient for the posts. (Check your trusted load tables; don't believe some random guy on the Internet.) If you replace some posts there is no harm in upgrading them to 6x6s, but I don't see a reason to sister onto the existing 4x4s.
However, it sounds like there is so much rot that it will be easier to tear down the entire deck and build a new one. If you do that, the new deck will of course need to meet current code requirements.
Uneven ground is very complicated for steps. You really want the distance from the last step to the ground to be uniform across the step, and the distance to the ground should be the same as the height of a step (i.e., if you have risers, the last one should be at ground level.
The right way to do this is to grade in the area of the steps so that a distance equivalent to at least several treads in front of the steps is level and then tapers gradually to meet the surrounding grade. You can do this by building up the low area, reducing the high area, or a combination of the two, which minimizes materials needed or needing to be disposed of.
You have some flexibility because a 7" riser is common but not a requirement. There is a relationship between the riser and the tread (2 x riser + tread = 26 to 27 inches). You generally don't want to go above an 8" rise, and a 10" tread is pretty narrow, so those factor limit the height. But you can go with long, shallow steps in the other direction, which is very comfortable to use. Here is a handy chart: http://www.gardengatemagazine.com/64stepchart/.
So you have several things to factor into a solution that you can adjust to best fit your situation.
- The ground has some grade, probably in several directions. Besides being uneven from side to side of the steps, it may slope as you move away from the steps. So how far out the steps come based on the tread size will likely affect the total height you need to transition with the steps.
- You need an integer number of steps, but you can adjust the riser vs. the tread to optimize the distance covered vs. grading requirements. For example, if the yard has a slope down going away from the deck, more distance covered by treads will require more total rise, so you might add an additional step to accomplish a more desirable step profile or to land at a point where the ground is more even so less grading would be required.
You can do this with trial and error calculations and a bunch of measurements of relative yard elevations at different points using a long level, or a board and a level, and ruler. The grade will not be perfect, so after you optimize everything, you will still need to do some amount of grading.
Grade to a little lower than you need. Install the stringers, supported by footers. Then fine-tune the grade. Lack of treads will give you access "under" the steps. Then install the treads.
Best Answer
The issue you are running into now is that end grains are poor for holding power. I would make 2x4 blocks 4” long and secure it in the corners underneath each side of the steps. The grain should run front to back, screw it into the stringer, then pull the stairs tight together, then screw the treads into the block; this will lock it into place.