1) "Bikesh Ya'akov lasheves b'shalvah..." Ya'akov wanted to have little quiet, but, says the Midrash, that is reserved only for olam ha'ba and is not attainable in this world.
In this world it's impossible to keep going up and up in constant growth. It's two steps forward and one step back (hopefully not the reverse). For tzadikim, they don't take steps back, but even they need to pause between steps on the ladder. There has to be six days of chol between every day of Shabbos.
Olam ha'ba is a different story -- there the breaks won't be needed and there certainly won't be backsliding. It will be "yom she'kulo Shabbos" without the need for chol in between. Kedusha will build directly and immediately upon kedusha; one Shabbos will follow directly on the heels of the next.
Rav Charlap explains that Ya'akov wanted the complete tikun to come about already and for this world to be perfected. He wanted that state of constant Shabbos, of total "shalvah."
Unfortunately, the world was not ready.
2) What's the idea behind Ya'akov giving Yosef a kesones passim? Was he really blind to the fact that it would be viewed as favoritism?
The gemara (Shabbos 145) says that the talmidei chachamim in Bavel wore fine clothes to look distinguished -- they all had frocks and up-hats -- while the Rabbis in Eretz Yisrael dressed like everyone else. The gemara explains that in Eretz Yisrael, the talmidei chachaim were respected and distinguished by dint of their Torah and personalities alone. In Bavel, the same was not true, and they needed clothing to distinguish themselves.
Ya'akov thought to himself that if the brothers think that he is sharing special Torah with Yosef and making him a bigger talmid chacham, the way to show that this is not true is to give Yosef special clothes, as if to say that he needs clothes to distinguish himself and the Torah alone won't do it.
3) One Chanukah question to get warmed up: the Pri Megadim (quoted in M"B as well) writes that an onein on Chanukah should preferably ask his wife to light for him, but if that is not possible, the onein should light for himself. He does not explain or address the obvious question: an onein is exempt from all mitzvos -- why is ner Chanukah any different?
I have no time now and it's not Chanukah yet anyway, so you have a head start in coming up with an answer and bl"n will come back to it.