Only the part about showing Forums and Categories on index (main site) are not working, everything else is working.
About the permissions, you're correct, it's a permission problem, thank you. It appears I jump this part on document 'cause I read fast.
I checked all the permissions to admin to make a test, and the Forums and Categories start to appear on index, but it come with another problem... the posts not appeared, all forums has "0 topics and 0 answer", otherwise, the AdminCP informs: Posts 89023.
I tried to resynchronize, recount and rebuild cache, but not works. But strangely, when I try to "Rebuild All" on "Rebuild Cache", the AdminCP shows: "Cached Posts: 0 of 89023 (0%).
I don't know why, but when I come to work I try to repeat process with Chrome (I previous used Firefox) and the conversion of users going well. But the Forums and Posts continue not showing on main page.