No, you pay tax on the value banding of your house and only the owner / tenant pays. So for example, take two houses of equal value within the same council boundary - one has 2 adults living in it and one has 4 adults. Both would pay the same yet the second house could effectively use twice as much council resource.
Debateable. It doesn't cost twice as much to empty a bin for a house of 4 people over the one with 2 in it.
I think some sort of hybrid council tax/poll tax set up would be fairest. One where the incremental cost of each additional member of the household is smaller and smaller, and the total tax reaches a maximum number of people, maybe 5 or 6.