Why are "Laue Spots" spots instead of rings? Or is there an effective way to estimate the number of Laue spots? I can't find any formulas or theory concerning this issue. Thanks for your attention!
Laue spots / rings are just the transmission mode analogue of Bragg diffraction spots / rings. A crystalline sample will show a spot pattern while a powdered sample (lots of small randomly oriented crystallites) will show rings.
See any entry level solid-state textbook (e.g. First chapters of Kittell) for a derivation of the "Laue condition" that determines where these spots appear.