It would help to incorporate trades to the automatic factory processes, if we could enable/disable trades with circuit signals.
I am not sure what would be the best way to implement this. My idea so far is that if a circuit config checkbox is checked, trades would only be enabled if the input contains the exact values of the selling side of the trade. Or maybe even the values of the buying side on the other input color.

This is achievable by putting circuit signals on inbound and outbound belts. Where circuit networks could help is there are two trades that take very similar items in the same hex core, but you still have a reason to use both rather than just one. In that case, you'd want an automated way of toggling them, which can't be done with belts. But, that's an extremely unlikely scenario, so I never added circuit controls to hex cores.

If I were to do it, though, I'd make it so that a circuit connection outputs signals such that normal quality signals represent inputs to the trade and uncommon quality signals represent outputs of the trade. That way, the inputs and outputs can be on the same color. However, it wouldn't be compatible with hex core inventory reading (which can turn off, but it'd be a wanted feature anyway). So, I would have to create a new custom entity just for emitting signals for the trade contents. Again, I don't think this is necessary because toggling belts or inserters is sufficient for almost all kinds of automation you could ever need.

You are right, my idea would screw up the core inventory signals. And most of the time can be handled by controlling input.
I have two situation in my game, where I wanted this:
One is what you said, on the same core
A item => B item
A => C
And I want both B and C items

Also, another core:
A => B
B => Money,
I have too much A, I need some B, and I want to convert the rest to money.

Offtopic, I wonder how different the trade random generator is between planets.
On Nauvis, I barely got anything useful.
On Fulgora, I have a great core generating more than two blue belt of scrap, and some extra concrete. Also some really useful cores to use up overproduction.
On Vulcanus, nothing useful for production, but two cores to slowly but surely generate money by an internal loop, with only initial input.
On Gleba, nothing really useful so far.

In the situation where you have A -> B and A -> C, which is what I described, like you said, I just thought of a way you could still use belts to control which trade is used: force a backlog by disabling output belts for items B (if you want C) or C (if you want B). This can generalize to M trades by disabling N outbound belts to prioritize M-N trades in a hex core where the inputs are the same item type.

Regarding the random item selection for trades for each planet, it's based entirely on the item values, which are almost entirely based on the various recipes in the game. Only raw resources like scrap and heavy oil on Fulgora or the ores on Nauvis have set values. Given that the multiplier of item values increases in the order of Nauvis -> Vulcanus -> Fulgora -> Gleba -> Aquilo, you'll find the most valuable trades on Aquilo and Gleba, and the least valuable trades on Nauivs or Vulcanus. But all planets have potentially useful trades just because they can involve the planet-specific items like bioflux on Gleba.

Yet, there's more to consider if you want to maximize coin production. Interplanetary trades (unlocked with silver item ranks) have a massive boost to the item values they contain. Combining that property with the specific multipliers to item values that each planet has, you'll find that selling Aquilo items like fusion reactors on Gleba will be the most profitable trade loop that can possibly be made, likely resulting in quick hexaprism coin generation. And, of course, consider higher quality selling (with high productivity from item ranks) such as rare or epic to scale that up to fully stacked hexic belts of hexaprism coins (450/s). Maybe.

Thanks!

It took me some time to understand your method of prioritizing trade by disabling output belts, but now it works. The missing part was limiting the non-filtered inventory slots in the core.

I am really far from the trade volumes you are talking about. But it is improving, slowly.
I plan to start on Aquilo soon, but I am probably too poor for that, and will need as many free hexes as I can get.

I have many items with two star level, but I only have two interplanetary trades out of 9581 normal trades. (BTW, the json export is really useful). Both on Nauvis. Is this normal?

Yes, that's a normal number of interplanetary trades. Claim every Nauvis hex to find all interplanetary trades. They are not discovered with some chance, but rather their positions are determined at the start of your game. Same goes for all planets. There is at least one interplanetary trade for every (initially non-tradable) item on every planet.