does all of buddhism depend on dependant co arising?

In the original Pali teachings, paṭiccasamuppāda refers to those conditions that dependently co-originate into suffering, as follows:

And what, bhikkhus, is dependent origination? With ignorance as condition, formations come to be; with formations as condition, consciousness; with consciousness as condition, mind-and-body; with mind-and-body as condition, the six sense bases; with the six sense bases as condition, contact; with contact as condition, feeling; with feeling as condition, craving; with craving as condition, attachment; with attachment as condition, becoming; with becoming as condition, birth; with birth as condition, aging-and-death, sorrow, lamentation, pain, displeasure, and despair come to be. Such is the origin of this whole mass of suffering. This, bhikkhus, is called dependent origination.

SN 12.1

It follows, paṭiccasamuppāda is called "the wrong path", as follows:

And what, bhikkhus, is the wrong way? With ignorance as condition, formations come to be; with formations as condition, consciousness…. Such is the origin of this whole mass of suffering. This, bhikkhus, is called the wrong way.

And what, bhikkhus, is the right way? With the remainderless fading away and cessation of ignorance comes cessation of formations; with the cessation of formations, cessation of consciousness…. Such is the cessation of this whole mass of suffering. This, bhikkhus, is called the right way.

SN 12.3

Anatta, sunnata and Nibbana lead to & are cessation; are the right path; are not paṭiccasamuppāda.

Pratītyasamutpāda considered to be Śūnyatā is only false, contradictory, the crutch, failure & hellish fall in Mahayana and particularly in the illogical utterances (rantings) of Nāgārjuna.

Those are just words.

These are just words.

How will anything be shown? With the crutch of useful words we make up ourselves or by the show of non-conseptual direct experience that just is?

The two seemingly contradicting realities(conseptual & non-conseptual) make it hard to explain the ineffable with words. There are multitudes of crutches in books that are useful but can't get one to the root of truth by themselves.

For your question, let us see Buddhism as an assemblage of three aspects of meditation, philosophy, ethics.

Dependent origination (paticcayasamuppada [Pali]) is a term used to make sense of things, the understanding gained out of meditation. The technique is not dependent on the concept or the word. The meditative technique remains as effective it is, irrespective of the fact that logical argument about a concept (which only connventionally makes sense) stands or not. So 'meditative' aspect of buddhism does not fall.

Sunyata and other concepts that you mention depend on this concept, as much as this concept depends on sunyata and other concepts you mention. {Refer to Mulamadhyamakakarika of Arya Nagarjuna} These concepts are part of a language-game being played, only so that the technique of meditation can be communicated to other people, so that they can understand and practice. If you show dependent origination to be false, you thereby show sunyata to be false. If you show sunyata to be false, it means you are saying things have an inherent existence (are not empty) or that you are saying there is nothing. Both these cases have been refuted extensively by Buddhist scholars (such as Arya Nagarjuna, Arya Candrakirti, etc.). If you say any of the above two cases as valid, you are not talking about Buddhism. But you are questioning about Buddhism. Therefore, you can't say things are have inherent existence or that things don't exist. Since you cant say either of these two, all you can say is that things are dependently originating. Since you would say that, you wont be able to say dependent origination is false or contradictory. 'Philsophical' aspect of Buddhism therefore doesn't fall.

Whether or not dependent origination stands or not, buddhists practice generosity, compassion, morality, etc. The 'ethical' aspect does not fall.

Thus, neither part of our aseemblage of Buddhism falls, therefore Buddhism doesn't fall.

It's not like "buddhism" "depends" on a "law" - it's just that D.O. is the most fundamental observation about how things work.

It is an observation about how the world of representation develops, from complete nondifferentiation to having appearance of distinct sentient beings who are born, die, suffer, argue and fight with each other.

And it's basically like, "hmmm, this appearance of distinct sentient beings with all their troubles only exists in the world of representation, and outside of representation none of this is applicable!" and "therefore, if we learn to deconstruct our own representation, we can transcend its limits and griefs" and "so, it makes sense to study how representation develops, this might give us clues into how to deconstruct it".

But if you want to prove it false, you'd need to prove false the very idea of representation (aka subjective experience aka consciousness). As well as the idea that subjective experience is something that does not just pop out of nowhere but grows over time.

Both of these are obvious facts known first-hand. We all have subjective experience. And we all remember how it developed when we were children. Do you want to try and prove this false?