Questions about images, universal knowledge and visual schemata in Kant's philosophy of mathematics

I am trying to understand what role images play in a Kantian account of cognition, with a particular focus on his examples concerning judgements about mathematics. This is a topic I am still quite confused about, so I thought I would write a blog post which is just a series of open questions I have.

Firstly, it's clear that Kant's notion of image¹ is not the same as the one I would naturally use (I consider an image to be a visual representation) - and so I'd like to better understand what he means when using this word. Kant sometimes talks about images being constructed in pure intuition, which I take to mean in the absence of any empirical sensation. This might imply that his notion of imagery is abstracted from any sensory modality, such that a feeling of five distinct points of pressure on one's skin is as much an image of the number five as five coloured patches arranged in space is.

It is also not yet clear to me whether images are supposed to only exist within the form of space or whether they can also exist within the form of time (as he implies in A142/B182), such that five distinct audible tones played in sequence would also be an image of the number five.

In all of these cases I'm also still unsure whether an image in pure intuition is one which exists at a sufficiently cognitively abstract level that it has no corresponding sensation, or whether it is just that any corresponding sensation that exists is imaginary rather than empirically given.

I'm also curious whether Kant's position is that images play a role in all mathematical judgement, or even whether they are necessary for making any particular mathematical judgement². In A140/B179 he seems to suggest that in order to make judgements about very large numbers we can shortcut the need to use images and just operate on schemata directly, does this imply that all mathematical judgements can be made without any direct use of imagery or just that judgements involving large numbers (or presumably also judgements involving complex shapes) can be cleverly broken down into smaller ones which can be reasoned about with imagery.

Finally I want to better understand what cognition involving schemata is supposed to look like. It seems to involve coming to understand constraints on the possible images a schema can generate, but I'm not sure whether this comes from the schema directly, or from observing some complete or partial images it produces, or from another source (the corresponding the concept? constructing a single image, and drawing conclusions from how it was constructed?).