No. No. May I ask where you thought this might be a good idea?
No. Toothpaste is not indicated for cleaning any part of the body aside from the mouth, teeth, and gums. There are products on the market that are indicated for feminine hygiene, although douching is not recommended because it eliminates helpful bacteria and leaves a woman susceptible to infections by yeast and harmful bacteria.
No. There are much better product is available to use for that.
Absolutely NO! Toothpaste is great for teeth. For feminine hygiene there are products specific, but consult with your doctor first. See your medical doctor if you have concerns regarding feminine hygiene.