IMac 2019: Can I mix the old modules with the new ones when upgrading RAM

Getting a performance boost depends on what you actually do with the thing. Run Activity-Monitor (Applications>Utilities) to see how much of your RAM is used. Most Mac stuff runs well on 4GB, but if you run memory intense stuff (Parallels-Windows, Video Editing, editing large pictures with photoshop) you should see an improvement. But even if you don't need the RAM, you should not see a performance penalty (i.e. it may or may not run better, but won't run worse).

Unless your computer is already slowing down to a crawl with the current configuration (when doing memory intense work), adding 2x 2GB should be enough (giving you a total of 8GB).

So, given your configuration, I'd add 2x 2GB to the free slots and keep the memory that is already there in the other slot.

As a general rule, you can mix sticks of RAM as far as brands/speeds/timings/sizes.

Your computer should accommodate different speeds/timings by scaling down speeds/timings on the faster sticks until they match the slower sticks.

Brands will matter as far as they do for everything else: everyone wants you to buy their brand of stuff, but they'll generally work. I've stuck random brands into random Apple/Windows machines and the ones that aren't just terrible do always work.

Depending how far apart the specs on your sticks are, you may have stability issues, but those are easy to fix - remove the stick you added.