The new Project panel Input LUT slot auto-looks in the Input folder. So there's less work in navigating to and selecting a LUT if they are in that folder. You can use the Technical folder, but then ... you would have to navigate to get to another one there or even the same one on a different clip.
The LUTs are applied the same no matter where they are stored, so your second question answer is no.
Understand, colorists call LUTs "the dumbest math out there" ... a LUT is a mathematical look-up table. X value becomes Y. That's it. And all LUTs are designed for a specific use. With media with an exact exposure and contrast level.
So if you have media that isn't exactly what that LUT was built for, then you will get the possibility of anything from too little contrast to clipped whites, crushed blacks, whatever.
That's why I never use the Technical folder for applying LUTs. You can't control what happens.
I always apply tech LUTs in the Creative tab slot, so I can use the Basic tab to 'trim' the clip's exposure, black/white points, contrast and sat into the LUT for best use of that LUT. Which is the proper process for working with LUTs taught to and by colorists.