This is a tricky one.
1. bbPress actually adds four different items to the Tools menu. The reason you usually only see one in the final menu is that bbPress removes the first three items later (they're used to register admin pages but are not shown in the final menu). However, Admin Menu Editor loads menu settings before bbPress removes those items, so they still show up in the editor.
Now, the reason why you don't see any of those items in the menu while AME is active is that two of the four items have the same menu slug. This is a bug in bbPress - WordPress documentation states that each menu item should have a unique slug. AME removes one of the duplicates and bbPress removes the other three items, so you end up with no bbPress-related Tools menus at all.
This is not really something I can fix on my end.
2. I can not reproduce this problem. I created a user with the "Author" role and the keymaster forum role and they could see and access the "Forums" menu without issue.