Hi Yoksel,
With an all latex mattress you will need a surface that has even rigid support and the gaps between the slats should be no more than 3" apart to prevent the very elastic latex from bending into the gaps over time and potentially reducing the long term durability of the latex. As long as you have this then you wouldn’t need a foundation or a bunkie board.
In the case of your bed … the slats are a little too far apart than I would be comfortable with so I would either add some slats to make the gaps smaller (it’s a good idea for the gaps to be about the same size as the thickness of the slats), use a bunkie board with more closely spaced slats (see here), or use something like the bed rug here in between the slats and the mattress.
Tranquility mattress uses high quality materials in their latex mattresses but they are not particularly good value compared to many other online manufacturers who use the same materials, have a better selection, better exchange options, and sell for significantly lower prices. Some of the members here who sell online and carry a wide variety of latex mattresses with better value are listed in post #21 here. There is more about Tranquility and some of their sister companies in post #2 here and some of the links it also contains.
While nobody can predict for certain how long any business will be in business … mattress warranties themselves are mostly meaningless because they don’t cover the loss of comfort or support that is the real reason that people normally need to replace a mattress. It’s much more effective to pay more attention to the quality of the materials in your mattress which will tell you much more about how durable a mattress will be than the warranty. Warranties only cover defects which will generally show up very early in the life of a mattress. You can read more about warranties in post #174 here.
Phoenix