Obviously you can't have a law that is binding on all people without an authoritative code that interprets and applies the law. That would be like having only the Constitution without the Supreme Court and legal code. The written law without the oral law would basically make everyone their own priest or rabbi and Judaism would end up like Protestant Christianity. That Deuteronomy 17 quote that you gave is what gives the rabbinic tradition its authority.
One other proof that I remember hearing that I didn't see on that list was the fact that in Zechariah 8:18-19 it states:
18 Again the word of the LORD Almighty came to me. 19 This is what the LORD Almighty says: "The fasts of the fourth, fifth, seventh and tenth months will become joyful and glad occasions and happy festivals for Judah. Therefore love truth and peace."
It is only through the Oral Torah that we get the institution of these fasts and the details on them. The written scripture makes no mention of fasts being instituted on these days, it only refers to them later. For Zechariah to make a reference like this indicates that the people were going by more than just the written law.
Yes but what happens if a Rabbi rules for a law to be Halacha that goes against Torah or strays from it, should we follow what the Rabbi says?
The halacha does not go against the Torah. The mishnayot accept the authority of the Torah as non-negotiable. And that is sensible considering the rabbis who said/taught the mishnayot were following in the tradition of the Sanhedrin and Anshei Knesset Hagedola before them who in addition to upholding and transmitting tradition from Sinai about certain major subjects, also expounded on verses to determine complex halachot in less clearly delineated subjects. The Written Torah is sacrosanct and no supposed "exposition" that did not accept its authority would be accepted as a valid exposition. The mishnayot are coming to expound upon the verses and give over mesorah. A Rabbi was not permitted to construct a mishna that went against the Torah. That could not be called a mishna, by definition. They had to stay within the rules.
And the Gemara actually then accepts the mishnayot as a canonical corpus. Rebbe Yehuda HaNassi established this canon by compiling all the extraneous mishnayot into an ordered corpus. He initiated the process of gemara which is the expounding upon the mishnayot, and at that point forward, the rabbis no longer were permitted to deviate from the instructions of the mishna or to create new mishnayot that argue on previous ones.
Rebbe Yehuda Hanassi's purpose in establishing this canon was to streamline and unify Judaism which was experiencing a great dispersal following the destruction of the Second Temple, a loss of centralized authority, and a developing divergence in practice based on the different schools of learning (quite simply a product of decentralized authority). So his goal was to create a sort of "replacement-Sanhedrin" to reestablish centralized authority once again based on the various halachic statements of the chachamim before him and in his time (all preserved orally), to unify Judaism and make sure that not only laws were not lost but that Judaism remained one religion. This was done not in the form of an actual Sanhedrin, but taking the ancient sources and statements of previous authorities learned in the yeshivot and making a canon out of them which gained acceptance among the scholars and would serve as the unifying factor while also being rooted in tradition - a new foundation from which to build upon. Of course, the new corpus opens up new opportunity for hiddush and innovation in the expounding upon these sources that constitutes Gemara. But there is always a balance between condensing and expansion. Needless to say, all of these sources depend upon the precedent of the Torah as the original canon which none can violate or argue with.