I love barbershop music ! Ocassionally its sung by fewer than four voice parts.
My dad is a barbershop singer but I barely knew him and so I don't know much about that at all. How old is that type of music?
The music itself began during the 1930s and is still present today !
My dad is nuts and I always thought it was weird that he sang that kind of music. Is it very popular?
Yes, particularly female barbershop quartets are popping up.  They are called the "Sweet Adelines" quartet 
Weird ok. I wonder where I can buy such music
I am not sure, although one characteristic feature of the barbershop harmonyis the use of what is knows as 'snakes ' or swipes'  Its a harmonic chord.
Do they always have to dress up in those silly little outfits?
lol i suppose thus the name. The music is either performed by the quartet or  a barbershop chorus