The VG Resource

Should I upload new sheets, or modify the old ones? (which were not made by me, and I haven't got the authors' permissions).

Ehhh, it would depend on how incomplete they are, in my opinion. Like if they're missing one or two tiles, it would probably be best to revise the current ones, but if several tiles are missing, I'd go for a brand new, more organized sheet.

Also, revising someone else's sheet is totally fine and major reason the revision system exists. If you're making significant changes, you can add yourself to the list of submitters too - just make sure the leave the original on there as well.

Sounds good. Quite a lot of the tiles are missing. Is it okay to redo the layout of it (keeping the original authors signature though)?

I don't see why not. If you're adding content to an existing sheet and need to shuffle things around a bit to make it work, I don't imagine there would be a problem.