Is it possible to play without mixed ore patches?

Yes! Check the mod settings.
Pie-chart ores: Disable Mixed Starting Resources and/or Mixed Resources.
Single ore type per hex: Set Resource Bias to 100.
Through gameplay: A Fulgora quest unlocks the ability to unmix ores.

Does this mod generate hexes and hex cores for modded planets?

Not until integrations are added. It is specifically designed and balanced around vanilla DLC planets.

Do modded items show up in trades?

Not yet. You can define values for items (which causes them to show up in trades) with the command /set-item-value, though. Be sure to run /help set-item-value to see how to use it. Also /get-item-value and /export-item-values and /import-item-values.
Sometime I'll make it so that modded items will automatically get valued on game launch (but this is much more difficult than it sounds).

What vanilla weapons does this mod buff?

Discharge defense, teslagun, destroyer robots. Each now function as tesla turrets.
Also defenders and distractors for range and damage, slightly.
Also there's a higher tier of bullets, railguns, and spidertrons if you really need some capable weapons for clearing dungeons.

Has anyone already made a script to find trading loops in the exported trades JSON?

Yes, I wrote a simple browser-based tool for this!