Tziporah was definitely allowed to get married From Hashem's testimony as Yevamos 122a says: A woman who hears from a Bas Kol (heavenly voice from a Malach communicating Hashems wishes Sotah 33a) that her husband died can get remaried.
ומשיאין על פי בת קול מעשה באחד שעמד על ראש ההר ואמר איש פלוני בן פלוני ממקום פלוני מת הלכו ולא מצאו שם אדם והשיאו את אשתו
With regards to inheritance from a deceased father we see with the daughters of Tzelofchod that when Moshe asked from Hashem who will inherit Tzelofchod, Hashem told him his daughters shall inherit him and they did following the testimony from Hashem. Bamidbar 36,2:
ואדני צוה בה' לתת את נחלת צלפחד אחינו לבנתיו
So so too when Hashem said:
וימת שם משה - "Moshe died there" (Devarim 34,5)
that meant that Hashem was telling Moshe's sons that their father Passed away and therefore this Passuk applied(Bamidbar 27,8)
איש כי ימות ובן אין לו והעברתם את נחלתו לבתו - "A man who dies and does not have a son his daughter shall inherit him",
So since Moshe had sons after he died they Inheritted him.
In fact According to Bais Shammai who argues (Yevamos 122a) that a Bas Kol cannot be relied upon, we have to say That Since Hashem declared "וימת שם משה" He was specifically telling Tzipporah to get remarried -just like Hashem forbade a Married woman to another man so too he can permit her- as The Passuk says clearly Devarim 20,7 that a woman gets remarried once her husband is classified as dead (see Kiddushin 13b):
פֶּן־יָמוּת֙ בַּמִּלְחָמָ֔ה וְאִ֥ישׁ אַחֵ֖ר יִקָּחֶֽנָּה