Can you extract specific compounds from infused oils?
THC is often extracted from cannabis by mashing up the plant with a solvent such as hexane. The slurry obtained may then be filtered off, and the solvent evaporate to give a crude extract from the cannabis which will contain the THC amongst other organic molecules.  Depending on the extraction solvent, the components of the cannabis plant are extracted in different concentrations, depending upon their relevant affinity for dissolving in the solvent. 

Coconut and olive oil have both been used in extractions, as they are safe for human consumption and so can be used directly once isolate without the need to remove potentially toxic (hexane) or flammable (hexane) solvent. 

In general, the solvents used are inert, that is, they do not react to degrade the extraction products as you mentioned. 

With regard to homeopathy, this too involves the extraction of active components from plant/biological matter. However, in homeopathy, it is generally less of an exacting science (for instance specifically getting THC out of cannabis) and more a case of extracting ALL of the components of a plant, for instance by making a tea. If you are interested in this, you might like to look at the recent Nobel prize winner Youyou Tu (2015, Physiology or Medicine). She realised that boiling the plant in water to create a tea was destroying the functionality of the molecule that chinese medicine was trying to extract, limiting its potency. By exploring alternative extraction methods she was able to get the biologically active compound without degradation leading to a useful drug.