'Blowing Dixie double four time' and 'He can play the honky tonk like anything' meaning

A honky-tonk was an old American term for a bar that played music, usually country music. Playing the honky-tonk probably refers to a honky-tonk piano, which is a piano that has been modified to alter the sound it produces, making it sound more tinny or percussive. It might also refer to the style of music being played. Play the honky-tonk like anything just means he can play it really well (see this similar question from ELL).

Savin' it up for Friday night just means that he isn't a professional musician, only playing occasional gigs (as indicated by the previous line, He's got a daytime job, he's doing alright).

Double four time likely refers to 4/4 time, which is a fairly standard time for music, also called common time. Cut time is 2/2 time, waltzes are played in 3/4 time. 4/4 means there are 4 quarter note beats per measure, 3/4 time is 3 quarter note beats per measure, 2/2 is 2 half note beats per measure. Cut time and common time are the same “speed”, but the beats are longer and less frequent in cut time.

As for blowing dixie, dixieland or dixie is a kind of jazz music from the southern USA, particularly New Orleans. This is suported by them playing “creole, creole”, as the creole culture is common in New Orleans. They tend to be played with a lot of brass and woodwinds, blown instruments.