Hi Waldamos,
I can tell you’re an engineer 
The first thing I would suggest is that there is no formula that can answer most of your questions with the kind of specificity you probably are looking for because the mattress is more for your body than your mind and your body doesn’t understand numbers or theory. I would avoid trying to design your mattress based on “theory” and would focus much more on how each mattress feels and performs in terms of PPP (Posture and alignment, Pressure relief, and Personal preferences).
I mentioned in an earlier post today that buying a mattress is much like buying clothes and while it’s important to know what the clothes are made of so you have a good idea of how it will perform and it’s durability … the most important part of buying clothes is how well it fits you and how it “feels” and matches your preferences when you wear them.
On to some of your comments or questions … but most of them will have an “it depends” in the answer.
FWIW … there are many people I know that could choose anything they want and are very knowledgeable about all the different mattress designs that would choose some version of a latex innerspring mattress over any other type. Of course there are also others who would make different choices but latex over springs can make a great choice for those who prefer this.
It depends on how you define “better”. Almost all latex is more durable than almost all polyfoam and it also has many other strengths that make it a unique material including it’s compression modulus (how quickly a material gets firmer as you sink in more), it’s point elasticity (how well a material contours to the shape of your body) it’s breathability (which affects temperature control), and it’s resiliency (springiness or ability to return energy from compression). You can read more about the pros and cons of latex in this article. both materials come in a wide range of firmness levels so one isn’t “softer” or “firmer” than the other because it would depend on your choice.
Having said that … both polyfoam and latex come in a wide range of softness and firmness levels so softness isn’t something that one material would be “better” than another although polyfoam can be made in firmer versions that you will usually find with latex although this level of firmness may not normally be very useful in a mattress.
No it has quite a different feel from most polyfoam (although some HR polyfoam is similar to some latex). It’s not only more resilient than most polyfoam it also has a different response curve and lower hysteresis and a higher compression modulus. Foam doesn’t have a linear response to increasing levels of force or pressure and the different response curves between different materials also have a significant effect on “feel”. Your testing will be able to tell the difference in most cases although the difference between polyfoam and latex (especially HR polyfoam) isn’t as much as the difference between fast response materials and slow response materials like memory foam and gel memory foam. Resiliency and durability aren’t related. There are some lower density foams that are very resilient but not very durable. The density of polyfoam and memory foam is the single most important factor in its durability. On the other hand almost all latex will be a durable material regardless of its density or formulation. Density is more connected to firmness/softness with latex but with polyfoam firmness and softness has little to do with density (every density of polyfoam has a wide range of firmness levels).
There is more about the many factors involved in relative durability and the useful life of a mattress (which are not the same thing) in post #4 here but in general a mattress will soften or break down from the top down and the closer to the surface a material is the more stressors it is subject to. The support layers are rarely the “weak link” of a mattress regardless of the type of material (within reason).
The springs are more an issue with the feel and performance of the mattress than they are with durability unless the mattress design has thinner comfort layers and the springs are taking up more of the compression forces in which case higher gauge wire would be more important. It’s the top 3" to 6" or so of a mattress that I would pay the most attention to (depending on weight and sleeping positions).
You can read more about the different types of latex in post #6 here but in essence it’s a preference and budget issue … not a “better worse” comparison. While they are “different” … one type of latex is not any “better” than another in terms of durability and the durability will depend more on the overall design of the mattress than on the type of latex that is used. Softer materials of any type will be less durable than firmer materials of the same type.
Outside of PPP … there is no “required thickness” of any material. The goal is “enough” to keep your spine in alignment and relieve pressure and to “feel” the way you prefer.
You will be able to tell if 2" is enough by testing the mattress and it will also depend on the springs. Some springs may be firmer and need more latex on top for some people while some (such as pocket springs) may be softer and need less material on top. With most springs there is an insulator over the springs to prevent the materials on top from sinking into the gaps between the springs but this generally isn’t necessary with pocket coils because they have smaller gaps and are individually encased and have a more supportive surface area.
One and two sided mattresses both have pros and cons. You can read more about some of the basic tradeoffs in post #2 here and in post #2 here (which are similar). If everything else is an apples to apples comparison … two sided mattresses will be more durable but they have less flexibility of design and this can also be offset by using more durable materials.
generally there is just air yes. On occasion there are inserts that can be added inside the coils or in the gaps between the coils for specific purposes (such as zoning or making some of the coils firmer) but this is not the norm.
My first choice in a foundation would be the foundation that is recommended by each manufacturer for their specific mattress. They are the ones who have to deal with any warranty issues and they generally don’t recommend a foundation that isn’t suitable. You can read more about using a solid support surface vs a more breathable surface in post #10 here but I would tend to avoid a solid support surface such as plywood unless there was a compelling reason to use it.
This depends entirely on the type of innerspring, the type and amount of all the other layers and components, the construction costs of the mattress, and all the other factors and policies that can lead to pricing differences in each area and with each manufacturer. The “value” of a mattress purchase is really a function of your personal value equation and involves much more than just the raw material cost of a mattress where you don’t know all the factors that are involved in the pricing of a specific mattress. I would always focus on the “value” of a mattress purchase but if you want to make material comparisons then it would involve comparing a mattress you are considering to other mattresses that are similar. This is another case where there are so many variables in the cost of each variation of every material and component as well as the many other factors that are involved in pricing that you really can’t use a formula and need to compare mattresses to other similar mattresses so your “value comparisons” are more relative than absolute.
As a very very rough guideline and bearing in mind that this is not in any way a reliable pricing guideline for any specific mattress … this article may be helpful.
Keep in mind that value is always based on many factors and dependent on what is available to you and what is most important to you.
This is really up to you to decide but it will also depend on the type of mattress you have and on how much it can be bent without damaging it. In most cases king size foundations are split for this very reason. Your own judgement and discussions with each manufacturer will be the best way to answer this one.
Whew … that’s a lot of questions but you’re very welcome and hopefully this has helped to some degree.
If I had to make a suggestion … as difficult as this will be for an engineer … it’s to focus more on your testing first and then to make comparisons between mattresses after you know more about which mattresses are best for you in terms of PPP. It’s much more effective to find the experts that already know what you would otherwise need to learn through a very long and never ending learning curve than it is to become an expert. From a technical level, the replies here have only scratched the surface and mattress design and theory is as much an art as it is a science. As much as you may want to reduce it to a science … the art that takes into account all the many objective, subjective and personal preference variables is just as important and it could be argued even more important than more technical information. While too little information usually leads to poor choices … too much information can lead to poor choices or even worse “paralysis by analysis” even more easily. The most effective time to do some analysis and comparisons are after you have narrowed down your choices so you can avoid trying to design your “best” mattress bases on specs or on information that can’t really be meaningful without more specific personal experience.
Phoenix