According to this chapter, what is the novelty of the commandment of fire on the altar despite the fire that came down from heaven?
In Halacha 1, Rambam rules that even though fire came down from heaven, it is a commandment to bring regular fire, as it is said, 'And the sons of Aaron shall put fire...'.
Question 2
How many fire arrangements were set up on the altar each day, and what is the purpose of the third?
In Halachot 4-5, it is explained that there were three arrangements, and the third is not for a specific offering but to fulfill 'a perpetual fire'.
Question 3
Who brings the two pieces of wood for the evening offering compared to the morning offering?
In Halacha 3: for the evening offering, two (plural 'and they shall arrange'), and for the morning offering, one (singular).
Question 4
What is the law regarding extinguishing a coal taken from the altar compared to extinguishing a fire designated for the pan or the menorah?
Halacha 6 distinguishes between the fire of the altar itself (liable) and fire designated for another commandment which is no longer 'the fire of the altar' (exempt).
Question 5
When is the time for the removal of the ashes on a regular day, on the festivals, and on Yom Kippur?
Halacha 11 establishes a hierarchy of times: regular—at dawn; festivals—earlier (beginning of the middle third); Yom Kippur—from noon.