1. I know that "Grenadier" nursery rhyme sans the "Knock-knock" and answer, as

"Who goes there?"
A Grenadier.
"What d'you want?"
A glass of beer.
"Where's your money?"
I've forgot.
"Get you gone - you drunken sot!"

(This was from a book, not folk transmission.)

2. I know one of the others cited above, again sans any knock-knock and not as a song (Calcutta, 1963, schoolfriend Dilip Palit):

What's your name?
Pudding Tame.
Where d'you live/
Up the lane.
What's your number?
Twenty-two cumber [?]
What d'you eat?
Friday meat.
What d'you drink?
Black ink.

Amazing, the fruits of colonialism.

Sanjay Sircar