I noticed that none of the categories assigned to the products were imported. Can I fix this?

Since you can import changes selectively this will be easy to fix. Most likely the problem is that you haven't pre-defined the categories in the Application settings > Product area. The second possibility is that the category names in the spreadsheet you are importing aren't exact matches. It is a common problem to have small differences, like calling the category "Shells" in Application settings but using the value "Shell" in the imported product rows. When categories don't match, they appear as red in the import screen.

To fix the problem, first determine what the mismatch is, then update the product properties selectively by importing just two columns from Excel: the Product ID column and the Category column.