Brining a food means to soak it in a salt water solution for a period of time.

sure

No they're usually injected with a brining solution, already, so more brining will make it too salty.

No, you don't have to cook a turkey, or any meat, right after brining. You'd want to remove the turkey from the salt solution, and pat the skin dry, and then put it in a container or some sort of packaging. (You don't want to leave it indefinitely in the brining solution.) You can also freeze turkey, pork chops, chicken parts, etc. after brining and not cook them for weeks or months.

its called brining.