Can intensive quantity be experienced?  Or, to put the question in the opposite mode, can our experience of intensity give us information about intensive quantities that we cannot experience? (In other words, is Schopenhauer’s thesis about epistemology of the will valid)

Following Delanda's reconstruction of Deleuze - intensive quantities are ones that are able to drive fluxes of matter.  Speed, temperature, pressure, and density are examples.  They are always differential - rates of change between two or more variables.   These govern all types of systems - machinic, social, ecological, geometric.  

What is affection?  Following Spinoza, an affect is an experience that corresponds to an increase or decrease in power (i.e. in "degree", which is an intensive quantity).  Thus a body inherently experiences joy when it enters into a relationship that allows it to grow closer to its essence. To some degree this feels intuitive in the human realm, but does it really extend to the non-human biological and inorganic realms?

It is worth noting that there is no consensus on the function of affect in humans.  We can follow Dan Siegel, however, in supposing that affection is actually the crucial "driver" of any and all information processing.  Affect is what awakens attention, memory recall and problem solving. 

If this is the case, though, then all information processing - whether human, artificial or natural - is driven by affect.   Some of the philosophers I am most interested in have an extremely dismissive stance towards the notion that "everything feels", but, in fact, if affect drives cognition in human beings (rather than being merely epiphenomenal, which is not very plausible) then it is hard to see how it wouldn't drive other systems.  

That doesn't necessarily mean that the affect needs to be consciously experienced in other systems (as shown by the fact that some layers of human affect are not consciously experienced but nevertheless drive cognitive processes).