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If one didn't light Chanuka candles until the second night, how many candles should he light?
According to the reason that we add a candle a night is "Maalin Bakodesh" (we always add in holiness), there is no reason to light more than one. If the reason is "Keneged [Yamim] Hayotzeim" (the amount of days that passed) one should nonetheless light two.
Do any of the Poskim discuss the Halacha in such a situation?
The Darkei Moshe (Rav Moshe Isserles's commentary to the Tur) discusses this issue in OC 672 sk 3. He quotes Rabbi Menachem of Reisberg (Merseburg?) as ruling that one who missed the first night lights only one candle, as it is his first night. However, Rema eventually rules against this and in accordance with Maharil (Responsum 28) that one who missed a night should light the regular way.
Although I cannot claim to have done a lot of research on this sugya, I am pretty sure that maalin bakodesh is not the exclusive reason for going from 1 through 8. Maalin bakodesh says that once you place something at a certain level of holiness, you cannot downgrade it. Lighting 1 candle every night would suffice to fulfill this requirement.
It seems that, even according to the 2nd opinion, all agree that there is a mitzva to show that there is a progression of 8 nights. Bais Shamai and Bais Hillel are arguing about how to show that progression. Bais Shamai held that it was more accurate to do a downward progression (perhaps showing how the oil burned- see Maharsha). Bais Hillel said that's a great svara, but unfortunately we have a rule of maalin bakodesh v'ain moridin. Bais Shamai argued back that we have precedent from parei hechag.
The upshot is that all hold of the daily progression, the only question is- which way.
I believe the active principle would be "don't separate yourself from the community." If all the other Jews in the world are lighting 2 then you don't go and light one.
Even according to Maalin BaKodesh you would light 2 on the Second night if you forgot the first night, as the question is whether you should start with 8 and reduce it by 1 a night or should you start with 1 and increase it over the 8 days. You will still be Maalin BaKodesh by lighting 3 on night 3 and lighting 4 on night 4 - so Maalin BaKodesh will still exist.
