Translation:My mother is shorter than me.
This doesn't seem quite right to me. I'd say it's actually: 母は (on the topic of my mother) 私より (compared to me) 背が低いです (is short)
The other guy only translated the nouns, leaning the particles untouched. So both of your breakdowns are good (presumably); they just have different focuses.
Is there an easy way to determine that it is my mother who is the shorter one in this sentence?
Whatever is right next to より is the one being compared to. So think of 母は私より背が低いです as "My mother (母), when compared to me (私より), is short (背が低いです).
Just leave out the "yori" part. Haha wa se ga hikui desu (compared to me - watashi yori)
The correct English translation is my mother is shorter than I. It's a truncated sentence. The full sentence would be "My mother is shorter than I am," not "my mother is shorter than me am."
The correct English sentence is the one that is idiomatic and can be understand. For the "truncated" version, that designation applies to both the version with "me" and the one with "I".
Huh? What's your point? The sentence was about the speaker and her(his?) mother. Bert never said you should use [母] when talking about somebody else's mother.
Also, I would appreciate it if you explained what you mean with saying that [母] is informal or casual. What would the non-casual or formal word for one's own mother be if [母] is a casual word?
If you're talking to your own family about your own family members: お母さん, お父さん, お姉さん（おねえさん）, お兄さん（おにいさん）, etc. If you're talking to other people about your own family members: 母（はは）, 父（ちち）, 姉（あね）, 兄（あに）, etc. If you're talking about other people's family members: お母さん, お父さん, お姉さん（おねえさん）, お兄さん（おにいさん）, etc.
This is correct. I xoild like to add if you would like to show more respect (e.g. a situation where you are talking to the total strangers) お母様、お父様,etc.
Why not "mum is shorter than me"?
Duolingo translates to American English. Maybe eventually it will have UK English too, but for now it doesn't.
UK English is accepted for any question where someone has submitted an error report and it's been approved.
The way I understand this, it says that as for my mom, the body is short, and mine is less so.