The possessive adjective (nostros) is needed here, as the subject (you all) is different from the possessor (we).
Contrast the sentence "We love our sons," where subject and possessor are the same, and thus there's no 'need' for the possessive adj. nostros (unless we want to emphasize, "We love our own sons.").
I never complained about a green light but now I must: I wrote "filius nostrus ..." and it was perceived correct, the "u"s not even underlined. When I saw the translation I was confused. Only now on the discussion site I see that I made a mistake. Please mark wrong vowels as wrong. Thank you.
Yes; the sequence -rus was replaced by -er systematically.
There's no magistrus, but there is a magister, magistri, m., schoolteacher, master; there's no agrus, but there is an ager, agri, m., field.
So, alongside feminine nostra and neuter nostrum, the masc. form is noster (genitive nostri).