After adding an applying a 3mm solidify i obtain the same results as you with the “check all”
But i don’t think those are real issues, but more to do with the object being very small.
By example in Edit Mode, select all and press S then type 10 (to scale 10 times) , the “Check All” will give Zero Faces being 0 , meaning that previously the 3D toolbox detected the face as being too small and considered them as “0 area” faces, despite they were obviously not.
This i don’t know if it’s a bug of the 3D Toolbox or if real 3D printers have trouble with object only a few centimeters big, that’s probably something to ask on a 3D printer website (or if they have a FAQ look into their acceptable dimensions)
For the thin face, look into the 3D Toolbox panel, it has the minimum thickness set to 70cm ! that’s ridiculously huge.
Lower that a lot, as if i look on one of the 3D printing website, they can accept much lower
If you change the 70cm into 2mm you’ll have no more faces considered “thin faces” (as the solidify modifier was set to 3mm anyways)
For the overhang, i have no real idea what cause this, i thought it may be the sharp angles, but some of the faces pointed to have a rather small angles, way below 45 degree , no idea if it is a real problem with 3d printing though, again better look on whatever 3D printing website faq if they talk about this