As far as the ship moving around, sounds like it is on explore. Select the ship and hit the explore button, that will toggle it out of explore mode. If you can't build anything else in a city that is because you will need either:
1. research new techs to get new building (or you may have just run out... the scenario does not give access to all the sandbox game's techs, etc.)
2. sufficient land space... make sure no tiles you want to build on are "swamp" if they are, cast raise earth on them.
As far as units not working, I'd guess the only way someone could help you with that is if you made a save game available (using dropbox and a link to file, or something similar) and a description of exactly which units are giving you trouble.