Chief Stoker is almost right on question one:
The unit (not ship) badge is worn on the left. They wear the MARCOM badge because that is their unit (These are the Admiral and his Command CPO).
AS for question 2, the Chief may not see a problem, but I, as an old ship's CO, do. In action, on the bridge with ten people running around equipment and station that are four feet high, facing partly away from me, wearing their anti flash gear and helmet, how the hell am I supposed to quickly find out if i'm looking at the OOW or just another seaman? Similarly, in the Ops room, looking over quickly towards, say, sea guard, if I can't see rank slip ons how am I to know if it's AB So-and-so or PO2 I-am-damn-good feeding me information? It matters to me.
As for badges, my understanding from the minutes is that the velcro will be different (Chief just beat me to it). However, we have never been allowed wear more than one Specialist Skill badge (at least in my days) on the Work dress/NCD. If you hold multiple qualifications, you wear the most relevant one to your job. So a Submariner who becomes a Clearance Diver will wear his clearance diver badge while so employed but can switch to submariner then she returns to service on submarine.