The awarded stars depend on the number of moves. The less moves, the more stars are awarded.
One should always take the parts that are not moving into account to solve a level with a low number of moves. Ideally, the next part can already be moved together with the current part. If a single isolated part is left towards the end, a lot of moves may be necessary to get it connected.
It may help to try different corners at the beginning, e. g. start with the upper left part, next time try to start with the upper right part. Sometimes it is possible to build a larger group of connecting parts right at the start and this is generally a good start.
In general, it is possible to solve every level, no matter how its parts where moved. However, if you get lost, you can always move back with the und button or go back to the start with the reset button.