Yes - German uses "jemanden um etwas bitten" to express "to ask someone for something".
Other examples: er hat mich um ein Taschentuch gebeten (he asked me for a handkerchief); ich bitte Sie um etwas Geduld (I ask you for a bit of patience; I ask you to be a little patient).
I suppose it could but the more common position for "darum" in the sense of "that's why" is at the beginning: "Darum würde ich sie bitten".
But even there it could also mean "That's what I would ask them for".
The "for it" is the "darum" -- to ask someone for something is "jemanden um etwas bitten" in German, and um + es = darum (just like "mit es = damit" and similar words).
So it's ambiguous.
It's similar to the difference between English "bit" and "beat".
bitten is [bɪtn̩] or [bɪtən] (the former is what I'd use in connected speech, the second a more careful pronunciation I might use in isolation) while bieten is [biːtn̩], [biːtən].
So the first vowel differs in both quantity (length) and quality (sound).
If your native language is Italian which has no lax vowel [ɪ], they might well sound similar to you.
But if you can distinguish English "bit, beat" or "ship, sheep" etc. then you should be able to distinguish German bitten, bieten.
And similarly for high back vowels: muss and Mus are distinguished as [mʊs] versus [muːs] -- the former has a short, lax vowel while the latter has a long, tense vowel whose quality is closer to the cardinal vowel and, I believe, to the Italian one.
That's not a correct translation.
bitten is to ask as in to make a request (he asked me to open the door, he asked me for the keys to the house), not to ask for information (he asked me about my mother), so "about that" is not an appropriate translation of darum in the context of this sentence.