Yes, Maritime and Mercantile can be good too.They are helpful, but some games they are not readily available. They are good to cut a few turns, but I don't think necessary. Maritime are just as useful. Mercantile, while not netting as much culture as pure city-states, can still potentially give you 10+ happiness, which translates into 5+ culture with policy. If culture city-states are not near, there should be useful alternatives.
Keep an eye on the resources available from the Mercantile though. With the latest patch, you don't get any extra happiness from them when going from Friends to Allies (instead you get the luxuries). It could be the case that you already have access to the luxuries that would be provided by a Mercantile CS, so in these cases, you can just stick with being Friends for the +3 happiness.
You are right that Religious CS can make up for the faith bonus of Stonehenge.If you have the time, then go for them. Why not? Else, I'd cut Stonehenge. Keep watch for religious city-state quests. Even just friends should be enough faith to get a religion up fairly quickly.
However, an early Stonehenge does mean that you are likely to get an early Great Engineer, which can be used to rush a later wonder that you really want.
Yes, that is right.1. Manually build monument, so Legalism gives you a free amphitheater.
The main scenario where I will want a free Legalism Monument in my capital is if my capital is in a prime desert location and I plan to get Petra (which also provides a free Amphitheater). So in this case I'd rather have a free Monument via Legalism.