My husband is the branch manager of the Osaka branch.
In this branch shop, there are workers who like to do things alone as well.
Our branch manager’s mustache is a bit too long.
The support shop is the branch office. Presumably this is because the regular "shop" is the "shop" and anything that supports it is the local (branch) office.
If it helps, this word has the same meaning as 支局 which you will also be learning in this level.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.