I find it interesting that your questions seem to relate to the usefulness and validity of this project. :-)
In any case, here are some quick answers . . .
The GM tube I originally used (shown in the pictures) was inside the plastic case with no vent holes. (It's a weather proof enclosure.) Nonetheless, there is no problem detecting highly penetrating gamma radiation. (Shipping containers are "x-rayed" with gamma.) The tube would also pick up some strong beta.
Later I replaced that tube with one capable of detecting alpha. Since alpha can be stopped by a piece of paper, I mounted that tube with the alpha window sticking out of the bottom of the case. I used gaskets to keep it weatherproof.
With both tubes I get similar variations in the daily counts as well as spikes. Since the creation of radiation is a random process, you have to be careful about making assumptions based on small variations. (I have not noticed a correlation between counts and time of day.)
I do get spikes every so often. What they might be related to, is an area of speculation I won't go into here. However, it's common to try to correlate spikes to the position of the jet stream, and solar activity.
The detection of radiation was only one facet of this project, the solar power budget, use of the transceivers, and logging are some of the others.
I've created many projects with the Arduino, and this was one of the most satisfying. Hopefully, some of the pieces and concepts may be useful to others.