Sefer Hatteruma addresses this issue (closely imitated in Hilchot Erets Yisra'el attributed to the Tur). They bring a few examples that prove that the ashes of the red cow were still in use after the destruction of the Temple, until well into the days of the amora'im, even though it must have been made while the Temple still stood.
Nidda 32a: Rabbi Yosi, ...
I heard an explanation in the name of Rav Shimshon Pinkus ZTL, as to why the Chachamim (sages) chose the Para Adumah as one of the places to discredit the opinion of the Tzedokim.
Based on RASHI BAMIDBAR 19:22:
פרה אדמה. משל לבן שפחה שטנף פלטין של מלך אמרו תבא אמו ותקנח הצואה, כך
תבא פרה ותכפר על העגל:
A RED COW — Why this rite was performed with ...
Rabbi Samson Raphael Hirsch explains in his commentary to Chukas that this command was chosen for the discrediting because it was such a public ceremony. The kohen was defiled deliberately before the ceremony's audience.
Perhaps the law only kicks in when it's given (i.e. at Marah and/or at Sinai) and is not retroactive, such that all red cows at the time of matan torah are eligible even if they worked the day before. Alternatively, perhaps because the Egyptians revered their livestock, there was at least a population of cows that were known to have never been used.
I remember an aggada in which a gentile sold a Para Aduma to the Sanhedrin and put a yoke on it just before he delivered it. The chachamim were able to tell that he had done so because it broke certain hairs on the back of its neck and those hairs would never grow back in the same way. I do not recall the source of this aggada, but it could point to the ...
The Artscroll Yad Avraham commentary to this Mishna only discusses lambs and rams regarding this "indeterminate status". In addition, at no point in their commentary to the mishna in 1:1 (which describes the various appellations of a cow) do they discuss any intermediate 30-day period.
The Rambam also does not mention the intermediate status of cows (Maase ...
Rashi Bamidbar 19.9
"למי נדה" - למי הזייה כמו (איכה ג) וידו אבן בי (זכריה ב) לידות את קרנות הגוים לשון זריקה
"חטאת הוא" - לשון חטוי כפשוטו ולפי הלכותיו קראה הכתוב חטאת לומר שהיא כקדשים להאסר בהנאה
Nidda addresses the fact that the waters are throwed. Chatas addresses two thinks, the first according to the pshat, that the waters clean, the second, ...
Some say think that there is a minumin amount something must be sprinkled (Zevachim 80a), but even they would agree that this applies to vessels, not people (Yoma 14a, Nidah 9a).
כַּמָּה יְהֵא בַמַּיִם וְיִהְיֶה בָהֶם כְּדֵי הַזָּיָה. כְּדֵי שֶׁיַּטְבִּיל רָאשֵׁי גִבְעוֹלִין וְיַזֶּה.
How much water is necessary for sprinkling? Sufficient for the ...