When it comes to groups or collections of people, how you refer to them can depend on how much you want to emphasise or deemphasise the members' individuality. This has been discussed on SE here.
Both "band" and "group" are collectable, countable nouns so all reasoning in the linked question applies here. There are times when a band or group "are in agreement" - and one cannot be in agreement with oneself, so it makes no sense to use the singular.
I think it would be quite acceptable to ask "What is your favourite band?", but in your example, it should be "are", because as you say the question must be phrased with who:
Who are your favourite band?
The band is a group of people, and when using "who" (as opposed to "what") you are emphasising the people rather than the collective noun.
If you were enquiring about a favourite solo artist you would ask:
Who is your favourite artist/singer?
You could answer either way:
Coldplay is my favourite band
Coldplay are my favourite band
One is simply referring to "Coldplay" as a collective noun, the other just highlights that there are individuals in that group.
Something else to consider is this possible follow-up question:
Who are Coldplay?
The answer from Wikipedia:
Coldplay are a British rock band formed in 1996 by lead singer and pianist Chris Martin and lead guitarist Jonny Buckland at University College London.
As you can see, the question always determines the answer.
I think the problem with this whole topic of discussion is that when people ask this question in real life situations they cannot possibly know what your answer will be. How do they know you love a band, and not a solo artist? You could be asked who your favourite artist is (singular) and reply with the name of a group! It is important to understand all this, but for the purpose of answering your grammar question I believe the correct answer should be "who are your favourite band".