I'm not a lawyer. This does not constitute legal advice.
You can mention them, yes. Nothing prevent you from doing this.
In fact, some license agreement require mention, and end credits is a good place to do so.
For trademark and logos, you need to find what guidelines the author has for using them. If there are no such guidelines, it is probably better you ask the authors about it.
In general is it OK to show the logos as long as it is a way the way its holders agree with. And you would want a legal disclaimer (something along the lines of making it clear that they didn't make your game, and you don't work for them, ask a lawyer about such disclaimers).
Screenshots of the software is a different thing. If the tool is open source (under a license approved by the open source initiative), then you would be in the clear to use screenshots.
Otherwise, I'd avoid doing it without permission of the authors to be safe. Although - in my personal opinion - legal action is probably not very likely because you are not competing with them. But remember that screenshots could include icons and other GUI elements that could be under copyright. It is also possible to argue that an screenshot is derivative work.
About the "free advertisement" approach, end credits is not the most visible place. You may consider selling a space in a splash screen, for example for an sponsorship. But that is an entirely different thing.
The flip side is, of course, that as I said above, some license agreements require mention. Which is common with free tools and assets. Thus, you can think of this "free advertisement" as what they get in exchange. Review your licenses.