Chinaski was 'pulling a sicky', taking a day off work becasue of excess drinking, something a lot of people have done at some stage during their life. So much so that certain companies have introduced 'Duvet Days'.
Dixie was a very famous song in America in the 19th century associated with the southern confederacy during the Civil War. With the Civil rights movement it became highly politicised, seen as an offensive song due to its roots in a racist past. It has often been boycotted for this reason.
Betty did die from all the alcohol abuse, it is commonly believed that the character Betty was based on Bukowski's first true love, Jane Cooney Baker.