Are abstract nouns always singular? Or are there such things as 'plural abstract nouns'?

Yes, there are plural abstract nouns. Here are a couple (emphasis, mine ... come to think of it, emphases is also a plural abstract noun):

state noun 1 The particular condition that someone or something is in at a specific time. ‘the state of the company's finances’ - ODO

• Frequency of positive states of mind as a moderator of the effects of stress on psychological functioning and perceived health - by Richard Bränström, published in bmcpsychology

stage noun A point, period, or step in a process or development. ‘there is no need at this stage to give explicit details’ - ODO

• I was in the early stages of pregnancy - ODO

From the list of nouns you were "in no way asking about", deserts, earnings, odds, damages and condolences are plural and abstract. Brains and guts are metonyms of concrete plural nouns.

What makes an abstract idea countable is the same as what makes a concrete noun countable: an accepted boundary to its extent. A pool (of water) can be distinguished from an adjacent pool because it has finite dimensions (you can tell where one pool finishes and where another starts). Likewise, there's a logical extent to ideas, states and stages, etc: you can tell where one of those finishes and another starts. On the other hand, the extent of air, water and flexibility is, in each case, somewhat nebulous, so they are treated as mass nouns. They can be quantised, however, and it's typically the quanta that are counted - e.g. a puff of air, a tract of water, a point of flexibility. Sometimes, the mass noun is used as a metonym for the quantum (e.g. in restaurants: 'one water' for 'one glass of water'), but this is straying outside the bounds of your question.

The issue with abstract nouns may be that extent is a conceptual matter there. One can't take a ruler to it or build a box to contain it. Nevertheless, if the abstract noun does have an (abstract) extent, it is countable.

Your question posits an exact correspondence of the abstractness/non-concreteness of a noun and whether it is countable. To define an abstract noun, the Oxford Dictionary uses three abstract nouns: idea, quality, and state. All three can form plurals. Flour, luggage, and celery are concrete, but not countable. How, then, can you support such a correspondence?

Ideas can be abstract, while nouns are always concrete if they can be used in a real (rather than imaginary) sentence.

The OED refers to concrete nouns that are used to produce an abstract thought (like idea, state or quality). People may refer to such tools colloquially as "abstract nouns", as a kind of shorthand, but that does not create a new class of nouns which no one can see, speak, write or hear. Words themselves are always concrete if they can be written down. What they mean is another matter.