We just happen to use a lunar calander and no, mewlid isn't based on the moon since it's not on the start or the end of a month. Ramadan for example is a whole month so when starting and ending we should check the moon, if the last month was a full one like 30 days or not like 29, the same goes for Eid , since it's also in the end of the month and we should check whether it's ending or have a plus one day. And for the emblem of the moon as much as I know it doesn't have much significance as the cross of Christians it's just a symbol to show the correlation with the lunar calander.