Is it permissible for me to shorten prayers (qasr) during frequent business trips, given that I reside on ships and floating hotels, and is it permissible to pray on these ships while they are moving, and does my frequent work count as an excuse for missing Friday prayer in the mosque?

It is sunnah for the traveler to shorten prayers and to combine Dhuhr and Asr, and Maghrib and Isha, either by advancing or delaying them, unless he intends to reside in the country he traveled to for four full days (excluding the days of arrival and departure). There is no difference in this between traveling for an act of obedience, trade, or work. If he does not intend to reside for this period, he is considered a traveler, and Friday prayer is obligatory upon him; it is not permissible for him to be preoccupied with work over it.