I can sing falsetto for short periods of time but it sounds terrible when I drag the note out. Can this be improved or am I stuck without falsetto?
In order to keep from developing bad habits it is much safer to work with a vocal teacher one on one. Falsetto is natural. From your description it seems you are lacking support. Full falsetto is a developed voice however baritones seem to develop it more freely. Are you a tenor or baritone or bass?