Hi Tudor,
Thank you for posting more images! They provide some additional details.
I am also a gemology student, so I apologize for any confusion I generate. Bare with me as I attempt to describe things and hopefully others will correct me and/or point out things I miss. 
Lets start with this image: 2024_1215_122740_007: If you zoom in slightly, you can start to see blue color bands that seem to be in straight lines. Color bands develop in the same direction as the crystal grows. This indicates one of the physical axes of the crystal structure.
When they are not curved or wavy, it is a good indication the stone is likely natural, but more information is needed to determine that.
It is possible the yellow hue is also from color bands, but usually on one of the other physical axis planes. This is what I was referring to regarding different directions (view points) or orientations of the color band lines.
The yellow could also be the base hue for the entire stone and the blue bands simply generate a stronger saturation for those patches (zones) with a blueish color. There could be some areas that are tinted with a greenish hue where the two zones merge or overlap based on the viewing angle. Looking at the stone from different directions, can show whether or not this is the case.
Here is a good article on crystal structures.
The immersion test, I mentioned previously, is a great way to see all kinds of features including color bands and growth lines. Water is a great fluid to start with but is definitely not the best for corundum and tourmaline. The test works better using a liquid that has a similar RI value to the stone. One of the forum’s members, @royjohn, has mentioned Benzyl Benzoate in various conversations. Benzyl is non-intrusive and is less likely to disturb or contribute to any treatments like dyes and/or oils that might be present. There are other household liquids that can be used as well.
Another interesting feature is in image 2024_1215_123034_012. The dark blob in the stone doesn’t seem to be visible in any other image you have posted. I am not sure what that is. Can you see it from other angles?
We can go over the RI tests you did to try and figure out why the birefringence is not vey observable. As you mentioned your refractometer may be a factor to consider, but there are some hints and tips to help even the most economical instrument perform as intended.
I know this seems to be a lot of information to throw your way, but I think it will help.
Cheers!
Troy