I have family members with cystic fibrosis. Is it possible to start show the symptoms in my 20's?

Yes. However, usually an adult who is diagnosed so late has usually had chronic problems with cough and "pneumonias". That said I've diagnosed a new case in a 38 year old woman.
Not likely. It is not likely. CF manifests during childhood, most often in infants, however, there are some forms of CF that are not diagnosed until later in adulthood (even though symptoms would have started in childhood). These particular forms of CF result in frequent sinus or upper respiratory infections, and can be incorrectly "written off" as chronic sinusitis or upper respiratory disease.