2. Regarding the filtering methods(search, tags, or start my search) pick one. If you don't know which one A/b test.
3. the highlighted navigation link should correspond to the page you are on to make navigation easier
4. the brands at the bottom (above the fold) are overkill. if you want to make this a thing, create a separate section allowing for more negative space above the fold.
5. the greyscale/ color scheme choices should be slightly more intentional, as an example the color around the tags below the "search a subject" would probably be better served as an off white or light grey similar to the navigation. part of this conflict is created with the brand area.
6. I would combine the "search a subject" input with the "show courses" button too. that way it is one complete unit
all I got for right now. cheers