I think you should carefully measure the extent of your UI, including elements, reaction of those elements to user interaction, usability in general, goals of your app, and so on. One thing that strikes me from your description is this part:
It is possible to use this color for links and main buttons, like
"Ok", "Sand", "Submit"(CTA buttons)?
It's very important that you differentiate between an ok button (usually found in a dialog, and generally a bad ux choice), a submit button and a CTA button, not to mention an error message! They're very different things and require different treatments. Not only color, but copy (specially copy!)
Getting to work...
Gmail (as mentioned in another answer) is a perfect example of the use of red in a button. This is because they want you to quickly see that button which is the most important in their app. You'll notice that button AND ONLY THAT BUTTON uses that color. You'll see links and a gmail dropdown using that color, but as long as buttons go, that is the only element, and it quickly stands out.
However, this is not appropriate for every case. In their case, they have a multi color logo so the button doesn't conflict with their logo and branding colors. In your case, the branding is red. So, common affordances like error messages aside, you should AVOID red and choose an accent. See your described scenario:
As you can see, everything has the same hierarchy, it's almost impossible to do a quick scan of elements. And here's why: you don't have an accent color, a concept that comes from architecture and furniture and is adopted by design. Google Material Color Guidelines recommends this:
Limit your selection of colors by choosing three hues from the primary
palette and one accent color from the secondary palette.
so we go to Gmail and... voila!
Since Google Material isn't the alpha and omega of design, you can easily use something like this:
you'll notice the green for buttons. This green is the exact opposite to your shade of red, but you could choose anything, of course.
Or, of course, we can follow Material guidelines:
There are many approaches to this. The important part is that you choose an ACCENT, therefore using red is not a good choice, despite affordance considerations