-- "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".