There was nothing wrong with the Book of Mormon people praying directly to Jesus while He was with them. The righteousness of their actions is attested by the Book of Mormon account of their praying to him.
Women do not need to cover their heads during prayer. Paul was giving counsel toward a local custom in order to avoid offense to any of the locals.
The measure of an effective prayer is sincerity not variety. The Lord does not like vain repetition nor “multiplying words” but taught simplicity in prayer.