Depends. You can buy iodine free from your local organic store.
Maybe. Pickles contain a lot of salt. Much of the salt used in commercially processed foods includes a small amount of sodium iodide in with the sodium chloride. So whether or not a pickle has iodine in it would depend upon whether or not the pickle-makers used salt with iodine, or plain salt.
Check the labels. As some may use a salt that contains iodine.