I dont think he had a co-commander, this was a navy ship and no doubt there was a second in command in case something happened to him. The ship carried an expert on merchant ships who may have been a civilian, I'm not sure, whose job was to identify any ships they found.
Lusitania was officially a british reserve cruiser and was built with money loaned by the british government. She was fitted with gun mounts but I do not believe with guns. The admiralty debated whether to call her up but the war did not go as expected. Her role would have been to fight similar german liners converted into armed cruisers too, but this didnt happen. The whole navy war as planned by both sides never happened. On the German side the navy crews slowly drained away as they were transferred to new submarines, and killed when the submarines were sunk. At the end of the war what was left of the German fleet, which was almost all the surface ships, mutinied. Probably very sensible of them.
Being on a surface warship wasnt exactly a safe job because they tended to go down or explode in the middle of the ocean and take the whole crew with them, but mostly they never fought so it was relatively safe compared to being in the army. But I would have thought most of U20's crew would have been killed by the end of the war.
That Lusitania was a reserve naval ship was well known. All cunard ships were at the service of the government and were preferred vessels for carrying government cargoes - presumably for security reasons. As I see it, the germans were quite correct that the ships were legitimate targets and the british made it impossible for the germans to sink them in a civilised way, allowing the people off first.
The US sent formal complaints to Germany about the sinkings. In the first place, formally, I think it was none of their business because it was a british ship which had been sunk, anymore than if some US citizens had been killed by bombs dropped on London. US citizens had no business being there. The US argued the Germans actions were illegitimate in international law because the Germans did not allow the people to escape, but as I just said, the British also failed to follow international rules whereby ships were not supposed to resist being siezed even by trying to run away, never mind by some of them having guns and shooting back. If the matter had ever come to a court case I suspect it would have been decided by whichever side got to appoint the judges, as is usually the case. Myself, I believe with admiral Fisher that rules about how to fight wars politely are ultimately futile. Fisher was once sent as british representative to treaty negotiations on international rules of war and spent his time blocking everything, as per why he was chosen for the job. But he was also a very charming chap so good at doing it politely.
I'm reasonably convinced it didnt matter whether this ship was identified as a merchant cruiser or not. That was something people argued about afterwards. All they were really interested in was whether it was a british ship or not, and if so then it was fair game. The Germans were trying not to sink ships of other nationalities but the british were making this difficult by instructing their ships to fly foreign flags.
Having said that, I am a bit puzzled why the Germans believed Lusitania was armed. On the whole they played fair under the rules and I must assume they were given information which said the ship was armed. If it never was, then someone made up false information and fed to them. It might have been useless spies who were paid to get information so just made it up to get the money, or it might have been the british feeding misinformation about their ships being armed. Which in a general way they did do, lying about how many had been fitted with guns. The polite explanation of why this was done would be to try to scare away german subs. The underhand explanation would be to put the germans in the wrong when they sank unarmed ships without warning believing them to be armed. Remember, Fisher was first sea lord and believed in total war. At the peace conference the Germans reported back on the british position as expressed by Fisher, which was that Britain reserved the right to do anything it pleased.