Do any of scholastic currents conclusively affirm or deny that there are any facts at all?

In original Buddhism, absolute truth, such as in the Four Noble Truths, are 'facts'. One interpretation of the terminology 'Four Noble Truths' is they are irrefutable, which is why they are called 'Noble' or 'Ariya' (which means: 'without enemy'). The scriptures say at SN 56.11:

...the Blessed One has set in motion the unexcelled Wheel of Dhamma that cannot be stopped by brahman or contemplative, deva, Mara or God or anyone in the world.

Those facts or absolute truths of Buddhism are considered to eternally & inherently exist, even if they are not comprehended or known by the human mind.

At SN 12.20 & AN 3.134, the scriptures say about the natural laws of the Four Noble Truths (Dependent Origination) & the Three Characteristics (impermanence, unsatisfactoriness & not-self):

...whether or not there is the arising of Tathagatas (Buddhas), this property stands — this steadfastness of the Dhamma, this orderliness (lawfulness) of the Dhamma...

In original Buddhism, the workings of kammic inheritance are not absolute truth or fact, since bad can be the result of good kamma and good can be the result of bad kamma (per MN 136).

It's not clear to me what your definition of "fact" is.

My definition of "fact" is literally, "something which has been done".

This definition of 'fact' says:

from Latin factum, neuter past participle of facere ‘do’.

... so it means "done" (for example, if you ask, "Is that a fact?", then I think that's the same as asking, "Is or was that done, did that happen?").

Furthermore a sutta like MN 60 Apannaka Sutta says that there is action:

Because there actually is action, the view of one who thinks, 'There is action' is his right view. Because there actually is action, when he is resolved that 'There is action,' that is his right resolve.

I think that this sutta is saying that, yes, there really are facts: there are actions, there are things done.

I think that to say otherwise would be a form of nihilism or solipsism.

I think (described is more detail here) that even the Yogacara (or "mind-only") school teaches that there are facts or conventional reality (albeit dependently-originated).

Since this question is epistemological, I will speak of knowers rather than objects of knowledge.

The Mahayana abhidharma defines seven types of consciousnesses. Lati Rinpoche says:

There are three divisions of awareness and knowledge: into seven, three, and two. The division into seven consists of direct perception, inference, subsequent cognition, correct assumption, inattentive awareness, doubt, and wrong consciousness.

The first four are realizing consciousness while the last three are not. A realizing consciousness realizes its object of engagement. A consciousness that does not realize its object of engagement can not be factually concordant. While an eye-consciousness seeing blue where there is blue is factually concordant (and an actual direct perceiver), an eye-consciousness seeing a blue snow mountain instead of a white snow mountain is not 'factually concordant' because there is no blue snow mountain.

A consciousness can be 'incontrovertible with regard to its object of engagement' and 'factually concordant'. For instance, a correct assumption is factually concordant (that is why it is correct) but is not firmly established (that is why it is just an assumption). It is not established in dependence on a perfect reason (contrary to an inferential cognizer, for instance). Because it is not firmly established, it is said to be 'controvertible'. All non-realizing consciousnesses are controvertible. A non-realizing consciousness can 'tend towards the fact' though: for instance, a doubt consciousness thinking 'all products are probably impermanent'.

Here, that 'all products are impermanent' is a fact. That 'there is a white snow mountain' is a fact. That 'blue is the attribute of such or such entity' is a fact.

Since you ask about 'scholastic currents affirming...', I will explain what 'a current' is. Mahayana scriptures explain four philosophical schools also called 'tenet systems'. The first two are so-called 'hinayana schools of thought' (Vaïbashika & Sautrantika) while the last two are called 'mahayana schools or tenets' (Cittamatra & Madhyamika). The meaning of 'Tenets' is 'established conclusion'. A person who propounds a tenet system is someone who has established conclusions in his continuum. For instance, he as come to established that 'all objects of knowledge are truly established, externally established', that 'all conventional truths are imputed existent while ultimate truths are truly existent', that 'there is no self-cognizer', that 'the four seals are valid', etc. He takes these as facts. For instance, a Buddhist monk disrobing and becoming a Christian monk is a person who had not established such conclusion in his continuum. His conviction was not firm, not based on proper reasoning, not derived from 'a perfect reason', not incontrovertible.

Generally speaking, he four seals are posited by all Buddhist tenets since it is what makes a school Buddhist. There are other facts as well that are posited, such as reincarnation, that karma is infaillible, and so forth.