"colmo" jokes are a set form of jokes, similar to the way we have "knock-knock" jokes, "blonde" jokes etc in English. Colmo can be:
last straw
height of stupidity
climax
limit
So...
What's the limit/height of stupidity/last straw for a rooster?
Asking for a pencil when he already has so many pens/feathers.
Which as you already mention, doesn't translate, because English uses two different words for pens and feathers.
Here are a couple more "colmo" jokes I remember:
¿Cuál es el colmo de Narciso Flores?
Que su hija se llame Rosa.
(Narciso means daffodil)
¿Cuál es el colmo de un albañil?
Que se llame Armando Paredes.
Albañil is bricklayer or construction worker.
Armando/armar means
to put together or
assemble and
paredes are
walls. But Armando can be a first name and Paredes is a last name.
About the use of cual. It's normally taught that it means which, but you basically have to learn how cual/que are used in Spanish because you can't always just use them in place of which/what in English (the rules are a bit different).
The use of an infinitive like that, is the same as the gerund (the -ing form of a verb) in English. In my translation I put
asking,
to ask is also correct. In this case,
pedir,
asking and
to ask are all nouns, serving as the subject of the sentence.
Hope that helps