YOSEF TOOK THE STATUS OF FIRST-BORN FROM REUVEN
בראשית מח, כב וַאֲנִי נָתַתִּי לְךָ שְׁכֶם אַחַד עַל־אַחֶיךָ
מסכת בבא בתרא דף קכג/א ת"ש והבכורה ליוסף וכי תימא יוסף גופיה ממאי דפי שנים כאחד הוה תא שמע ואני נתתי לך שכם אחד על אחיך א"ל רב פפא לאביי אימא דיקלא בעלמא א"ל עליך אמר קרא אפרים ומנשה כראובן ושמעון יהיו לי
Yosef received two portions similar to two of the portions of each of the other brothers (one for Efraim and one for Menashe). It is understood that the first-born status was transferred from Reuven to Yosef as a result of the actions of Reuven in moving the “bed” of Yaacov.
How is it possible to take away the rights of first-born, since that is against Halacha? It is possible to understand this from the Ramban. The verse says not to remove the rights of the first born from a son of a hated wife to the son of a beloved wife. Ramban says this is not possible על פני, while the son is alive. But after death, the first-born rights can be removed from the inheritors. In our verse, it is also referring to the rights that occur after the death of Reuven (the future division of Eretz Israel); thus, it was permissible for Yaacov to remove the first-born status from Reuven (taking effect after death).
KING FROM THE HOUSE OF DOVID
בראשית מט, י לֹא־יָסוּר שֵׁבֶט מִיהוּדָה
ירושלמי מסכת סוטה דף לז/א פרק ח הלכה ג אין מושחין כהנים מלכים. אמר רבי יודן ענתונדריה על שם (בראשית מט) לא יסור שבט מיהודה.
Optimally, a king is appointed from the House of Dovid. However, if no fitting candidate exists from the House of Dovid, or for other reasons, a King may be appointed from another tribe. However such a King does not cause to inherit the Kingship to his children and he is also not anointed with oil. The Gemura’s citing of the Cohanim teaches that one might have thought that the Cohanim are very spiritual and already have leadership qualities, nevertheless, if a Cohen becomes a king, not being from the House of Dovid, he would not be anointed.
SEVEN DAYS OF MOURNING
בראשית נ, י וַיָּבֹאוּ עַד־גֹּרֶן הָאָטָד אֲשֶׁר בְּעֵבֶר הַיַּרְדֵּן וַיִּסְפְּדוּ־שָׁם מִסְפֵּד גָּדוֹל וְכָבֵד מְאֹד וַיַּעַשׂ לְאָבִיו אֵבֶל שִׁבְעַת יָמִים
ירושלמי מסכת מועד קטן דף יג/ב פרק ג הלכה ה גמרא מנין לאבילות שבעה מן התורה, שנאמר ויעש לאביו אבל שבעת ימים
How could we learn a law from prior to the giving of Torah? Thus, the Talmud Bavli derives from another verse (Amos 8) הפכתי חגיכם לאבל, just like the standard holiday is a 7-day period, also mourning is a 7-day period. Perhaps, the difference between the two Talmuds would be reflected in regards to the status of מלאכה during Chol HaMoed, if compared to mourning or not.
According to the consensus, these cited verses are only a אסמכתא, and the 7-day mourning period is a rabbinical decree. According to the Torah the law of mourning applies only to the day of the burial.