Plant matter can definitely be composted. It might not be a bad idea to neutralize acidic plant refuse, using calcium hydroxide or sodium bicarbonate, especially if the compost will be used for plants that prefer slightly alkaline soil. If acetic or hydrochloric acid was used, then the acid could simply be evaporated out of the plant matter.
Basic water can be poured down a drain. It wouldn't hurt to neutralize it, but keep in mind that NaOH is primarily sold as a drain cleaner. So not only is it unlikely that it will damage your pipes, it might actually clear them out a bit!
Small volumes of solvents commonly used for extraction that cannot be used again (i.e. those used to defat an extraction) can be mixed with a small amount of an absorbent, I have heard of people using additive-free kitty litter, dried and then disposed of with household garbage.
Larger volumes of solvents, or halogenated solvents would have to be picked up by a local household hazardous waste collection program. Many recycling centers and garbage dumps also have the means to dispose of solvents and other household hazardous waste.
In the past I have evaporated solvents, then scraped up the oils/fats and anything else that was dissolved in the solvent and flushed it. But I have since been told that evaporating certain nonpolar solvents can have an impact on the environment. I'm not completely certain that it does, but better safe than sorry.
I have also heard of people flushing small amounts of solvents used in an extraction down the toilet. I am not positive, but I can see how this might be damaging to the environment as well.