To answer your first question,
I'm not sure what kind of chemicals store bought roses are usually treated with.
Short answer: a lot. These flowers (especially when they're roses) don't really have much room for defects, so pesticides are applied heavily as a preventative, even when there are no symptoms of disease or pests on the plants.
Most of these are going to be fungicides (roses are prone to many fungal diseases), especially when these flowers are grown under glass, where pests aren't as big a problem as they are outside. The plants were grown fast in an unnatural environment, using lots of simple chemical fertilizers, then treated with systemic (intaken by and circulated throughout the plant) pesticides, so they are kind of laden.
You can compost them, they'll decompose, but they will have a lot more pesticide residue in/on them than the average compost item.
About the flower feeding packets, these usually contain:
- Dextrose (sometimes glucose), a sugar, to provide energy to the plant as there will be little photosynthesis going on
- Citric acid (or another acidifier) to bring the water pH down to that of the plant, so that it can take up more water. Also, it helps keep the pigments in the petals stable longer (slower fading)
- Chlorine/bromine (or another biocide) to keep microbial activity low. The microbes feed on sugar, which will be concentrated at the stem bases (from the intake process), so microbes can clog the cuts, leading to a rapid decline in the cut flowers.
As for dumping it in your compost pile, it probably won't have any noticeable effect, but it does contain biocides, which might be counter productive in the decomposition process. I wouldn't dump it in my compost pile, but that's my personal preference. You can look at the list above, and make that decision for yourself.