In terms of the verb agreeing with the number, you need to be clear about what is doing the verb.
For example, "A number of people are waiting for the bus", it is the people who are waiting, and there is more than one person, so use are. Here using "a number" could be replaced by "some".
However, when it is the number that is doing the verb, eg, increasing, then it should be singular.
Eg. The number of users has increased.
But what about "the numbers of users...". Here you would use are, but why would numbers be plural? Are we talking about more than one groups of users?