Those are compulsive habits, and not easily stopped.
I picked and bit my toenails, but not my lips. IMO there is a little anxiety involved in compulsive habits, so try and make your daughter's home life as calm as possible, and don't make too big a deal over the habits.
What she's doing won't ruin her lips, but try buying her some cute chapstick. Maybe that'll help.
Try putting a bandaid with lots of Neosporin on the infected toenail, and if the nail isn't too ingrown that will take care of it. If the nail is seriously ingrown, you have to have the doctor fix it. When I was a teen I was always causing toenail infections by my picking, and the bandaid/Neosporin trick always worked for me.