1- Minimum Snow Load in Purlin Design
According to ASCE 7-22 [1], balanced and unbalanced snow loads shall be evaluated separately. For purlin design, the unbalanced snow load cases are similar to those used for main frame design; however, the applied load for purlin design shall not be taken as less than the minimum snow load, Pm.

In practice, however, designers often use the unbalanced load cases developed for main frame design for both the main frame and the purlins.
For example: when Pi= 6.6 psf and Pm= 30 psf , the value of 6.6 psf may be appropriate for main frame design; however, 30 psf shall be used for purlin design. Using Pi= 6.6 psf instead of Pm= 30 psf for purlin design can significantly underestimate purlin demand, leading to substantially lighter purlins that are neither safe nor code-compliant.

References:
[1] American Society of Civil Engineers. "Minimum design loads and associated criteria for buildings and other structures." American Society of Civil Engineers, 2022.