What is the significance of the three levels of Hidur that the Chachamim established for Ner Chanukah?

The Brisker Rav (Chidushei ha'Griz, Hilchos Chanukah) asks: How could the Chachamim make an enactment of Hidur Mitzvah, beautifying a Mitzvah, by lighting an additional flame each day? The Gemara in Bava Kama (9b) says that one is only obligated to perform Hidur Mitzvah up to a maximum expense of one-third of the cost of the Mitzvah itself. Here, the Hidur Mitzvah is many times more (a total of 36 lights, instead of 8)!

Beis Hillel maintains that the "Mehadrin Min ha'Mehadrin" way to perform the Mitzvah of kindling the Chanukah lights is to "add progressively" ("Mosif v'Holech"). Does this replace the "Mehadrin" level, in which one candle is lit for each member of the household, or supplement it?

One who performs the Mitzvah in "Mehadrin Min ha'Mehadrin" fashion will light 36 candles on Chanukah. What is the significance of this number? Why do we begin on 25 Kislev?

What insight can we derive from the opinions of Beis Shamai and Beis Hillel, as to whether we decrease or increase the number of candles each night?

According to Beis Shamai, one lights Chanukah candles in regressive order (eight on the first night, seven on the second night, etc.), just like the Korban Musaf of Sukos decreased by one each day. Is there a connection between Chanukah and Sukos?

One rationale for Beis Hillel's opinion is, "Ma'alin ba'Kodesh v'Ein Moridin - we ascend in holiness, and we do not descend." But do two lights have greater holiness than one?