Are all of the five aggregates saṅkhāras?

The word "saṅkhāra" has many meanings, such as:

1. "Compounded things formed by causes & conditions"

2. Mental aggregate of thinking & creating (sankhara khandha)

3. "Mental proliferating of thought".

4. Etc; etc; etc.

This old blog may help; although I need to re-read it for accuracy.

Therefore, as "compounded things" (meaning #1), each of the five aggregates are saṅkhāras, as follows:

Rūpaṃ kho āvuso channa, aniccaṃ, vedanā aniccā, saññā aniccā, saṃkhārā aniccā, viññāṇaṃ aniccaṃ, rūpaṃ anantā, vedanā anattā, saññā anattā, saṃkhārā anattā, viññāṇaṃ anattā, sabbe saṃkhārā aniccā, sabbe dhammā anattā

Form, friend Channa, is impermanent. Feeling is impermanent. Perception is impermanent. Mental formations (saṃkhārā) are impermanent. Consciousness is impermanent. Form is not-self. Feeling is not-self. Perception is not-self. Mental formations are not-self. Consciousness is not-self. All (sabbe) conditioned things (saṃkhārā) are impermanent (aniccā). All (sabbe) phenomena (dhammā) are not-self (anattā).

SN 22.90

Being compounded things, they must be impermanent and originated from causes (idappaccayatā).

It is important to distinguish between idappaccayatā and paticcasamuppada; otherwise we will fall into Mahayana by using the term "dependently originated" inaccurately.

Paticcasamuppada is about how ignorance manifests over 12 conditions to cause sorrow, lamentation, pain, grief & despair and the whole mass of suffering.

Idappaccayatā is the general principle of cause & effect. Therefore, a physical eye, for example, is formed via idappaccayatā because it is made from atoms, neurons, skins, etc. Merely for the physical scientific reasons a physical eye is made up of different physical parts is why it is a sankhara. The interaction of the mind is not necessarily for the physical eye to be a sankhara.

Again, the more we fall under Mara's spell of Phenomenology; the more we spin around and around in questions. The spell of Mara is like this; dragging into samsara.

If all five aggregates are indeed saṅkhāras, then what is the aggregate called "formation" (saṅkhāra)?

Please read this answer for more info on sankharas based on Bhikkhu Bodhi's essay "Anicca Vata Sankhara". I quote the TL;DR version from that answer:

Sankharas are "co-doings," things that act in concert with other things, or things that are made by a combination of other things. Ven. Bodhi uses "formations" or "volitional formations" as his preferred translation.

There are 3 uses of the term Sankhara in the scriptures:

1. Second link in dependent origination - when ignorance and craving underlie our stream of consciousness, our volitional actions of body, speech, and mind become forces with the capacity to produce results, including "rebirth".
2. The fourth of the five aggregates - volition regarding forms, sounds, smells, tastes, tactile objects, and ideas. Also covers all factors of mind except feeling and perception.
3. All conditioned and compounded things including mountains, fields, and forests; towns and cities; food and drink; jewelry, cars, and computers.

The only thing which is unconditioned and uncompounded is Nibbana.

Are the five aggregates all saṅkhāras -- are they impermanent and dependently originated?

Yes, in all the different meanings of sankhara, they are always impermanent and conditioned (depend on other things for their arising and ceasing).

Are "form" and "consciousness" dependently originated, and what (conditions or causes) do they depend on?

MN 148 explains the arising of consciousness:

"Dependent on the eye & forms there arises consciousness at the eye. Dependent on the ear & sounds there arises consciousness at the ear. Dependent on the nose & aromas there arises consciousness at the nose. Dependent on the tongue & flavors there arises consciousness at the tongue. Dependent on the body & tactile sensations there arises consciousness at the body. Dependent on the intellect & ideas there arises consciousness at the intellect. 'The six classes of consciousness should be known.'

Meanwhile, form as one of the five aggregates refers to body, and it being conditioned and compounded is explained in MN 74:

Now, Aggivessana, this body — endowed with form, composed of the four primary elements, born from mother & father, nourished with rice & porridge, subject to inconstancy, rubbing, pressing, dissolution, and dispersion — should be envisioned as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a disintegration, an emptiness, not-self.

Does "eye consciousness" exist when there's no contact? In a blind person, for example?

According to SN 12.44:

Dependent on the eye & forms there arises eye-consciousness. The meeting of the three is contact. From contact as a requisite condition comes feeling.

"Contact" in this quote refers to mental contact and not physical contact. When there is physical contact between eye and forms (in this context, "form" means visual objects), eye-consciousness arises. The meeting of the three would result in mental contact.

This is only my speculation, but presumably, a blind person can see darkness or black.

Is it right to call e.g. the doctrine of the "four noble truths" a dhamma instead of a saṅkhāra? Is the doctrine unconditioned and not subject to decay

According to AN 3.134, the Dhamma does not depend on the coming of a Buddha:

"Monks, whether or not there is the arising of Tathagatas, this property stands — this steadfastness of the Dhamma, this orderliness of the Dhamma: All processes are inconstant. ... All processes are stressful. ... All phenomena are not-self.

According to this essay by Ajahn Sumedo:

Akalikadhamma means that Dhamma is not bound by any time condition. The word akala means timeless. Our conceptual mind can’t conceive of anything that is timeless, because our conceptions and perceptions are time-based conditions, but what we can say is that Dhamma is akala, not bound by time.

Is awareness of (e.g. perception of) the dhamma a saṅkhāra, which depends on contact (e.g. contact between mind-object and mind-consciousness), and impermanent?

While the Dhamma (teachings) may not be sankhara, the mental concepts built around it definitely is sankhara, which is why seeing it through wisdom (through vipassana) is needed, as compared to intellectualizing it.

-- "Are the five aggregates all saṅkhāras -- are they impermanent and dependently originated?"

In my understanding, it's the experience of "my life" that is a saṅkhāra - while the five aggregates (lit. "heaps") are called that because they are an analytical classification of the experience into functional groups, they do not exist as anything separate to begin with:

The Elder said: ‘A hard thing has the Blessed done, great king.’

‘Which hard thing has the Blessed done, venerable Nagasena?’

‘The hard thing the Blessed has done, great king, is the analysis of all the formless dhammas - of the mind and everything related to mind - that unfold on the same foundation: here is Phassa/Contact, here is Vedana/Feeling, here is Sanna/Recognition, here is Cetana/Intention, here is Citta/Thought.

‘Give me an example.’

‘For example, great king, someone were to sail out to the open sea, and taking some water in the palm of his hand, were to taste it. Would he be able to tell: here is water that came from the Ganges, here is from Jumna, here is from Aciravatī, here is from Sarabhū, here is from Mahī?’

‘That would be difficult to do, venerable.’

‘That which the Blessed has done, is even more difficult, great king - the analysis of all the formless dhammas - of the mind and everything related to mind - that unfold on the same foundation: here is Phassa/Contact, here is Vedana/Feeling, here is Sanna/Recognition, here is Cetana/Intention, here is Citta/Thought’

The ocean metaphor used by Nagasena in Milindapanha serves to illustrate that our normal experience is completely unified, just like the water in the ocean is an indistinguishable blend of waters from multiple rivers. Separation of the fire of experience into the five heaps of fuel is an analytical exercise. The heaps themselves do not really exist as something distinct from each other.

-- "...I guess that "perceptions" and "feelings" are perhaps dependent on sensual contact. Is there anything else they're dependent on? Are "form" and "consciousness" dependently originated, and what (conditions or causes) do they depend on?..."

Yeah, of course they are all impermanent and dependently originated. In fact in one of the suttas Buddha talks about this at length, pointing out how each of the five heaps is not reliable because it depends on some fluctuations outside of one's control. And yes, that included consciousness which depends on external stimuli (here, "rupa").

-- "Does "eye consciousness" exist when there's no contact? In a blind person, for example?"

As @ruben2020 correctly said, it is Contact that depends on consciousness, not the other way around. This is because Contact is phenomenological contact, the experience of coming into contact with an object of sense.

And yet, as you correctly intuited, consciousness is not something that abides - it is an emergent phenomenon that is ephemeral and discontinuous. Continuity and integrity of consciousness(-es) of individual senses, experienced as one seamless whole is a convenient illusion. IMO consciousness is not a good translation for vijnana for exactly this reason - because it implies that it is something abiding that cognizes stuff. Instead, consciousness is ephemeral representation of a stimulus in the mind based on the stimulus relationship with sankharas - imprints left by the previous experiences.

-- "If all five aggregates are indeed saṅkhāras, then what is the aggregate called "formation" (saṅkhāra)? What is the difference in the meaning in the word "saṅkhāra" when it's used to identify that one aggregate, as opposed to when it's used to characterise all aggregates"

The sankhara which is one of the five heaps is called so because it represents aggregation/accumulation of experiences over time, leaving imprints or memories, these imprints then acting as latent tendencies determining person's impulses and reactions. In both cases the word sankhara (lit. "together-made") means something that is constructed or assembled from multiple elements.

-- "Is it right to call e.g. the doctrine of the "four noble truths" a dhamma instead of a saṅkhāra? Is the doctrine unconditioned and not subject to decay ... or is this a theory about Dhamma (i.e. a meta-dhamma) proposed by some schools and not others?"

The Teaching is called Dharma because it expounds the universal law. Indeed, in Chinese Buddhism the word for Dharma is usually translated as "The Law" or "The Rule". That said, in Mahayana Buddhism the fact that even The Teaching itself is conditioned and relative is universally recognized.

-- "Is awareness of (e.g. perception of) the dhamma a saṅkhāra, which depends on contact (e.g. contact between mind-object and mind-consciousness), and impermanent?"

My teacher said that "Enlightenment is only a phenomenon, too" - so here you go, this piece is also "a saṅkhāra, which depends on contact (e.g. contact between mind-object and mind-consciousness), and impermanent".