The missions cannot be skipped and are not linked to a specific city. If you don't/can't complete your current mission on your current level it will be available on the following level(s) until it is complete.
For missions requiring a specific number of the same building to be built (i.e. 4 Starbit Coffee) you need to have all of the buildings in your city at the same time to complete the mission. Once a desired building appears, you can tap on it and check the historical box. This makes it so the same building is always built on that lot. This can be helpful for missions requiring specific buildings to be built or if you want to groom your city to look a certain way. When you are done with that mission, you can uncheck the historical box to allow the lot to be rebuilt to a different random building from the available pool the next time it is rebuilt.