@gordon contributed a patch to the gtk3-classic project which aims to bring back some of the stuff we liked before GTK+3 became a thing.
Just recently, we now have packages for Ubuntu 19.10 too!
If you install this "patched replacement" for GTK+3, you'll just want to add some styling locally; restart Caja and the treeviews will be back to their zebra stripe look!
thank you, lah7,
for the link and your contribution!
It took me a while, but I finally scraped together the time needed to get you the third patch. Happy -- um, 12th of January holidays, anyone? 
This patch is intended to be applied to Caja 1.26; it probably will not work on Caja 1.24 as-is, but that shouldn't be an issue for you since you use 1.26.
Here's the patch:
Now, unfortunately I cannot provide you with further presents like this -- you'd be surprised, but I'm in pretty high demand right now, so I can't spread myself too thin. Unless you'd be willing to pay €10 for the next patch... 
Still, if there's any problems with this latest patch, please let me know. I tested it myself, and if you don't find any problems with it, I'll be submitting it to the MATE project "upstream" soon, hoping that the patch will make its way into the next release of Caja! I've already submitted the previous Caja patch you requested to upstream, and it's gotten some attention -- and I've made minor corrections to the patch as requested by the MATE developers themselves:
I look forward to seeing you try out this latest patch, and hopefully it'll work for you! I see no reason why not...
EDIT: Oh yeah. This patch will not immediately change the automatic folder expansion behavior; the patch only adds such an option to the Caja Preferences, and when you turn that option off, the automatic folder expansion is then disabled. Here's where you can find the new option:
Thank you again, dear Gordon! It works great! But it seems this patch and patch #1 rewrite their settings vice versa. I cannot have both concurrently.
When you compile the caja package, at the point when you run the patch command, run one patch command with one patch as a parameter, and then run another patch command with the other patch as its parameter. Example:
patch -p1 < [path to patch #1]
patch -p1 < [path to patch #3]
Otherwise, the steps are the same.
I hope that helps.
Oh, there's a misunderstanding, sorry. I did not mean the patches concurrently. I meant the resulting functions in caja. Making the first patch I have no problem with the panes but after patching #3 I have the folder funktion but the panes issue is back. And that is vice versa.
I found that if I applied both patches and then compiled Caja, I could use both feature additions. I do not see what you are talking about, unfortunately. Again, if you want both feature additions, you must download the source code, apply one patch, then apply the other patch, and then compile the doubly-patched source code. You cannot expect to get both features by downloading, applying one patch, compiling, applying the other patch, and then compiling again.
Please allow me to demonstrate what I think you should be doing:
mkdir BUILD
cd BUILD
sudo apt build-dep caja
apt source caja
# Apply *both* patches...
patch -p1 < [path to patch #1]
patch -p1 < [path to patch #3]
# *then* compile the code.
debuild -us -uc -b
sudo apt-get install ../*.deb
If the above doesn't work, or that's what you're already doing, then I'm not sure what's going on. Maybe paste the output of those two patch commands into a new post here, so that I can see exactly what's going on.
I'm sorry this is such a struggle. I hope for the best for you.
I found the solution! The problem was with "gtk+3 classic" which I installed earlier. After purging the ppa and reinstalling the patches all is working perfectly! 
Maybe you give the guys there some information.
Thank you, dear Gordon, for your great patience guiding me!
Please take a look at my problems and the solution I found.