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.
Satan cannot hear the thoughts of our hearts when we pray silently. We are commanded to pray vocally as well and should not fear Satan but trust God.
Don’t confuse custom with principle. Customs change from day to day, and Mormons believe it is important to respect the customs appropriate to the age in which we live.