With regards to the video, The Rogatchover would often give halachic reasons for stories in the Torah (see the Samplers in this article). Here's one example.
Bereishis 22:6 - Before the Akei'dah, Abraham loaded the wood on Isaac, but not the knife, because there is a disagreement between the Talmud Bavli (Pesachim 66a) and the Yerushalmi (Pesachim 6:1) if it is permissible to lean the knife on the sacrifice once it has been sanctified. Abraham wanted to make sure that every detail of his precious korban was perfect, and was scrupulous to fulfill all halachic opinions.
I guess one could argue about whether this was actually Avraham's intention or if this is just a "pshat", but I'm pretty sure it doesn't deserves the ridicule given in the video.
As a proof that Torah was learned before it was given, our sages point out that if Noach didn't have Torah, how would he know which animals were pure, and which ones were impure. (many other similar proofs are brought as well)
With regards to the questions and contradictions between the laws in the Torah and the actions of the Avot, R' Chaim Volozhin, in Nefesh Hachaim Sha'ar 1 Chapter 21, says that when our sages say the Avot kept the whole Torah (in this he included Amram as well, not just Avraham, Yitzchok and Yaakov), they didn't do so because they were commanded to do so. If they were commanded to do so, they would never violate any of the commandments of Torah. Rather they understood with the great Tikkunim that are accomplished by doing the Mitzvos, and the destruction the would be caused by them not fulfilling the Mitzvos. So they always made sure to do the actions that they understood that their souls would cause Tikkunim.
Therefore, when for example, Ya'akov Avinu saw that his soul could accomplish amazing Tikkunim in this world by marrying two sisters (since he understood that it was specifically through them that the Jewish nation would be brought into this world), he worked hard to make sure this happened. So too, Amram married his aunt so since he understood that doing this would bring Moshe Rabbeinu into this world.
And that's one of the reasons why the Torah wasn't given to the Avos, since if they already had the Torah, it wouldn't matter if they realized that great Tikkunim could be accomplished by going against the Torah, they would not be able to do so.
R' Shneur Zalman of Liadi, explains in Torah Ohr (page 134 "Moshe Yidaber...") that every Mitzvah brings down a different revelation of Godliness into this physical world (which is why Mitzvos are done with physical objects and actions). The Avot were able to draw down this same revelation even before the Torah was given. This is what it means that the Avos kept the whole Torah even before it was given. However, the Avos brought down these revelation spiritually, not physically.
In a footnote to his father-in-law's Ma'amar, the Lubavitcher Rebbe notes there were some Mitzvos that the Avot only kept spiritually (e.g. Tefillin, which mention the exodus from Egypt, which hadn't happened yet), and some Mitzvos that the Avot physically performed. Even the Mitzvos they did physically however, were only able to draw down Godliness into the spiritual worlds, the physical item they did the Mitzvah with remained unchanged.
As an example, the Zohar says that the sticks Ya'akov used to affect the look of the sheep born (Genesis 30:37 and on) was how he spiritually observed the mitzvah of Tefillin. However, once he was done the sticks did not retain any holiness and could be thrown away (unlike our Tefillin). See here and here.
The Lubavitcher Rebbe (Likutei Sichot Volume 5, page 146) gives a very practical reason why Avraham waited to have a bris. Rashi explains that G-d's commandment to Noach after the flood, forbidding spilling a mans blood (Genesis 9:6) applies to spilling ones own blood as well. As such, Avraham was legally unable to circumcise himself until G-d explicitly commanded him to do so.
Also, I once read and explanation of the Lubavitcher Rebbe that even Rabbinical Decrees are the will of G-d. If so, why aren't they recorded in the Torah? Because it was G-d's will that they be Rabbinical and not Biblical.
There are differences if a Mitzvah is Biblical or Rabbinical. For example, in the case of a doubt. When you have a doubt whether the prohibition applies, in a Biblical Mitzvah you must be strict, but with a Rabbinical Mitzvah you may be lenient.
Also, at least according to some opinions, when something that is Biblically prohibited the item itself is prohibited, whereas when the item is Rabinically prohibited, the prohibition is on the person, not the item (Gavrah vs. Cheftzah). See here.
If so, it makes sense why the Avot kept even the Rabbinical Decrees, since they too are the will of G-d, not just decrees that the Rabbis created later.
See here as well for many of the major commentaries of whether the Avos kept the Torah or not.