Translation:My mother said not to borrow money from the bank.
母 does not carry any honorific sense so it can almost only be used on one's own mother in a familiar way. If the subject is the mother of the person you talk to, you can never used 母，at least you have to use お母さん(okaasan) to show your respect. So there is no nuance in here.
This is correct, thank you.
For all, reporting the sentence will go to the course contributors for evaluation. Sentence discussions are primarily for users, so we can discuss why something is or is not correct. It's a learning tool for us. :)
Would a course contributor consult the sentence discussion while evaluating? Possibly. If someone was unsure of, for example, US vs UK usage, I imagine that they might. I'm not a contributor, so I couldn't say. But they don't use these to source new accepted translations, if that makes sense.
Thank you all for helping each other out! Is one of the things I love about this community.
Direct and indirect speech are not as easily distinguishable in Japanese, as they are in English, particularly for the unquoted Japanese sentence. The subject of the sentence is "my mother" and the quoted sentence is in command form, so I feel it's equally right to interpret this particular sentence as a direct quote in English.
Multiple sources indicate that it isn't as clear as you indicate. https://japanese.stackexchange.com/questions/30584/direct-and-indirect-quotes https://goo.gl/oXPy1D https://link.springer.com/chapter/10.1007/978-3-642-00609-8_13
母[My Mother]は[PRT.TOPIC/Regarding]銀行[bank]から[from]お金[money]を[PRT.DIRETOBJ]借りないで[SEE NOTES]と[PRT.QUOTE]言いました[did say]。
借り [かり]: (P, n) borrowing, debt, loan
借りる [かりる]: (P, v1, vt) to borrow, to have a loan, to rent, to hire
ない [ない]: (P, aux-adj) not (verb-negating suffix; may indicate question or invitation with rising intonation), (P, adj-i, suf) emphatic suffix (after the root of an adjective)
ないで [ないで]: (aux, conj) without doing ..., (aux) used in sentence-final position as an indirect prohibition
Is how I try to understand it, hope it helps.
Right so, in this case, the で is the te-form of the verb. The te-form has many uses, but here it is an abbreviation of でください, which I'm sure you know is a polite way to make a request.
Here is a link for to-form conjugation rules: https://kawakawalearningstudio.com/all/exactly-te-form-japanese/
...actually, this link doesn't cover the negative te-form, but to do that simply replace ない with ないで or なくて (not なくで!). That's what this sentene is using.