"Request" means the same as "order" or "ask for."
There are shades of meaning with words. "Order" and "request" most definitely do not have the same meanings or connotations to a native English speaker.
I believe you have mistaken the context for "order"...it's order as in ordering food in a restaurant...it has the same meaning as "ask for" or "request" in this context.
As a brazillian, I find sometimes the duolingo voice a bit scary. Particularly in this example, she seems very upset.
Why do you not need a preposition after 'pedi'?
Prepositions work differently from language to language... in Portuguese, you usually use "pedir + noun".
ah okay, thank you!