"My father and mother are from Osaka."
That would be more like saying "my father and mother are ALSO from Osaka". Perhaps if someone had just told you they were from Osaka, this would be an appropriate response.
But if you are only saying that your parents are from somewhere, you want to use と and は like given above.
父と母も大阪出身です。 would be 'My father and mother are also from Osaka (in addition to another party).'.
とbetween two subjects makes a pair.
（父と母）はお金持ちです。My mother and father are rich (as a couple).
（父も）（母も）お金持ちです。My father is rich and also my mother is rich (separately).
The following is from a [Japanese Q&A site:]*https://www.bengo4.com/c_3/c_1340/b_49625/)
'I'm discussing divorce with my husband right now. After we divorce, as my father and mother are also divorced, I want to take my mother's (maiden) name. Is this possible?'
In another comment section here on Duolingo, somebody asked why 'も' is used in this sentence instead of 'は'. Then someone gave an explanation as to why 'も' doesn't always mean "also", and why it is more appropriate to use 'も' in this case instead of 'は'. Either I'm processing the information wrongly, or there are arguments clashing all over the place.
For the 'mother and father are well' example, the answer (using 'mo') was closer to 'my father is well and my mother is also well'...
using 'mo' indicates they both have the stated attribute separately / independently.... using 'to' indicates that they 'share' the stated attributes as a single unit...
While there are other words to refer to one's own father/mother, using these particular words (ちち・はは）does give the context definitively that you are referring to your own father/mother. [Does not require 私の. In fact, that would sound redundant]
（X）のお母さん - X's mother
（X）のお父さん - X's father
両親 （りょうしん）My parents / Parents as a general concept.
（X）のご両親 - X's parents.
I think it's because Japan is a very patriarchical society (certainly historically), so the 'male'aspect comes first... it's the same reason why the masculine 'they' is used for mixed groups (because the men in the group are 'more important' than the women).
You see the same logic in e.g. Spanish and other languages that explicitly assign gender in their language.
No - leaving the honorifics off when speaking about your parents to someone else is a way to indicate humility etc... you're implying that you and the people associated with you (such as your parents) are less important than the person you're talking to.
The focus in Japanese is being polite to the person you're talking to, not being polite in how you refer to people you're talking about... at least as far as honorifics etc.
Oto-san and okaasan are the respectful honorific form of saying it. You'd use that to refer to someone else's father or mother to show respect. Chichi and haha to refer to your own mother and father since it's more humble I guess.
Think of it as similar to being respectful and calling someone's dad and mom Mr. X and Mrs. X. Not calling them by their first names or "X's dad/X's Mom". Same mentality.
私の is not redundant, but not necessary. 来ます is not used for past tense. 私の両親は大阪からです。私の両親は大阪生まれです。私の両親は大阪から来ました。My parents are from Osaka. / My parents are Osaka-born. / My parents came from Osaka.
In the last example, coming from Osaka indicates that they just traveled from Osaka. This does not mean that they were originally from there.
Also, Duolingo wants to be sure you know how to say mother and father, not parents.
Finally, しゅっしん is used often to inquire as to someone's origins. It is the default and should be used in this case.