"She told me nothing."
Translation:Hon berättade ingenting för mig.
No, you have to use the construction above, "berätta X för Y", where X is what's told and Y is who receives the telling.
ingenting needs to go before för mig, but you can say inget just as well as ingenting, there's no difference in meaning in this case.
There's a difference between inget and ingenting in that both can mean nothing, but only inget can mean no. For instance inget bröd is 'no bread', and you can't use ingenting instead.