Hi Joy,
Most latex manufacturers keep their compounding formula a secret for competitive reasons so you won’t be able to find out the exact formula or chemicals they use to make the latex but the most effective way to assess the “safety” of any material is with the testing certifications they use or by requesting a sample in case you are sensitive to one of the ingredients they use in their formula that wouldn’t affect most other people. All the latex you are likely to encounter (natural, synthetic, or a blend of the two) has been Oeko-Tex certified or Eco-Institut certified so for most people they would be a very safe option even for those that are very sensitive.
They can yes so it would be a good idea to use a dust mite encasement around your mattress, foundation, and pillows to keep them from multiplying in your mattress, keep out the skin particles which they feed on, and to protect you from their feces (which is the main dust mite allergen) as well. There is more about dust mites in post #2 here and about dust mite encasements in post #2 here.
There is a huge range of different futons and materials that are used inside them (just like mattresses) and I would evaluate them for “safety” and durability based on the materials inside them just like I would mattresses. A few of the better sources for futons I’m aware of are listed in post #2 here which includes a number of natural and organic options.
The best approach I know is to follow the steps in the tutorial post one at a time … and take your time and ask the questions you need to ask so that you are comfortable (literally and figuratively) with the choice you end up making.
Phoenix