Is a 7 degree slope for a roof too small in a rainy area?
It depends on the type of roofing you’re going to use. 

Its steep enough for single-ply membranes. We use single- ply membranes down to 1/4” per foot. 

Make sure you have adequate (large enough) gutters and downspouts. 

I live in a area that has a significant amount of rain (60” or more per year) and we have a few downpours too. I’d use a 4” gutter and 2 - 2”x 3” downspouts for your carport.