Can I create form categories on my Console website?

Yes, it is possible. One suggested way is this:

1. First you would create a page for each forms category (in WEBSITE> PAGES).
2. In each page you would create the list of forms belonging to that category: write the name of the forms in the content editor and insert the link (with the "Insert/Edit link" button from the content editor) to the appropriate form using the "Link List" drop-down list in the "Insert/Edit link" pop-up window.
3. Then you would go to WEBSITE TAB > MENU and, under for FORMS menu/tab you would delete the existing submenus leading to each form and replace them with submenus for your forms categories (click on the green plus icon labeled Add submenu) to which you assign the appropriate forms category page created in step 2 above (from the Page drop-down list in the Add submenu pop-up window).

This way, when your clients will hover over the FORMS tab from client perspective, the drop-down submenu will show the forms categories and your clients will click on the forms category page they are interested in to access the forms. You could also create a single page with all the forms categories and link it to a sub/menu on the client website.