Absolutely right to not push traffic from the final approach just because a faster one is behind them. That is bad ATC.
Downwind is fine, and as bookworm says, some give and take is required.
No instructor should send a pilot solo until the pilot can fly all this stuff. This is one of the stupid things about PPL training: the strong emphasis on "going solo" as early as possible and you don't grow the proper CAA approved hairs on your chest until you have been solo. People sitting in the bar looking all despondent if their first solo has been delayed. So people are sent solo when they can only just about manage to fly a plain simple circuit without crashing down. If you were training somebody you care about to fly, you would never do things this way round, and the latest work in the USA (taking a student through a whole PPL/IR using a scenario based approach) supports this.