Hi,
Thank you very much for the details!
Can you please add temporary back-end access details, so I can check out the issue directly?
The one with the color picker button is very likely only a CSS related issue. Probably a Salient module is loaded on the Ajax Search Pro back-end, where it should not be, and CSS rule could hide the button. I have seen this issue only once before (it was not related to Salient), and it was an unwanted CSS file with a global rule hiding buttons.
The other one with the drop-downs might be more problematic. If it is a script fiddling with the boxes, that might need to be resolved from their side.