No you don't need a permit
No
No. Your NY learner's is not valid to upgrade to a Texas license. You would have to get a Texas learner's permit.
As long as you are conforming to the limitations and restrctions of your NY learner's permit, you can legally drive in any state.
No. You'll have to start the permit process over again.
yes your permit works around the united states
You must be 16 to apply for a permit and be liscensed.
.7
Contact the issuer of the permit.
No, you'll have to start all over again in NY.
A NY pistol permit doesn't serve as a carry permit. As far as carry permits go, New York is a "may issue" state, which pretty much translates to, "we don't issue, unless you have some serious connections and can throw lots of money at us".
You'd have to be a resident of VT, and you'd pretty much have to go through the process again... unrestricted drivers licenses are reciprocal and can be transferred right over - this does not hold true for learners permits.