Search several columns and cells and pull data from one cell into a separate table?

I'm attempting to find eligible students for a higher level class and need to check for the prerequisite classes to be completed, and not sure how to get the end result that I need.

Firstly, I need to check a column (H) for several classes and to check the cell next to those classes (I) to see if thev've been completed.

Then, if those classes have been completed, I need to check another column (G) to see if the percentage is less than 100% and greater than 0%

If so, I need to add the students name associated with those classes (B column) into a separate table (K)

I'm not sure what the best route to take here is. I will add an example table in the comments for reference. The formula needs to work regardless of how the columns are organized/filtered.

Excel version : 2508