Cavities are caused by sugars (and sugars only), so in theory, if you just eat green vegetables and meat, you shouldn't get any cavities. Veggies contain fibers and the consensus is that they exert a light brushing action on teeth (think when you chew celery and such)

A great resource for these questions is nutritionfacts.org (free and full of references to scientific studies)

As for toothpaste, what you do is ok, the only risk you run is to overdose on systemic fluoride, which sometimes causes diarrhoea. An alternative is to rinse with a mouthwash and not rinsing with water afterwards