You dont have to understand how quaternions work internally to use them.
To use them you just need the provided functions and their documentation.
As a rule of thumb, euler angles only exist for human comprehension. They are a convenience. If you work with rotations, you usually want to just forget them and directly work with quaternions, using the provided API. When you work with euler angles, it should be a read-only process. Either for yourself, or some simple comparisons / thresholds. If you want to write them, you should keep track of the euler angles (persistantly) in the background. Never convert quaternion to euler, work with that, and then write them to quaternions again. A quaternion maps to more than one euler value. The only reason you dont notice that in the inspector, is that unity put extra effort into making sure these stay consistant. For human comprehension, since the inspector is used by humans.
There is very few, usually highly specialized, people on the entire planet who properly and fully understand quaternions and the actual relation between their x, y, z and w values. It is a topic of complex mathematics (C, the number space above R). A four-dimensional one at that. Pretty hard to mentally grasp, not that i claim i do, despite having worked with several related topics back at uni.
As for your core problem, this does indeed seem like a problem between the coordinate systems of unity and blender. They use differing coordinate systems, as such.
Blender:
X-Axis: Points to the right
Y-Axis: Points forward
Z-Axis: Points upwards
Unity:
X-Axis: Points to the right
Y-Axis: Points upwards
Z-Axis: Points forward
You have to export models correctly. I rarely if ever work with blender, but there is plenty of tutorials for that. Afterwards just make sure you dont have weird rotations in your object hierarchy. You probably want it to be 0,0,0 before applying rotations. Otherwise you need to put the model in a child to apply a static rotation to it, and then rotate the unrotated parent instead of this child. That way you can apply this static rotation to all custom rotations.