I'll try to explain it.
Is there a tumor in your humor?
It means smth. like " Have you no/bad sense of humor? "
"tumor" is in rhyme to "humor", that's why author uses it.
No special meaning.
Are you getting on a bit?
smth. like "Are you making progress?" Not "too much progress", but "a little", "a bit".
I got my back up.
get someone's back up = to make someone get angry.
Do you need a bit of rough?
It means smth. like "Do you want, that your life would always be without any troubles? Or do you need some (troubles)?"
rough = roughness.
But "rough" can be either a noun or a verb. "Roughness" can only be a noun.
She likes to switch teams.
She changes her opinion, friends, depending on what is better in this moment.
Or maybe she is a football coach and likes to change teams.
Hope it helps...