Why not pairs? If you don't put a breeding box in they won't breed. But you'll be missing out on a large fun part of birds. If you do put breeding boxes in and actually get some babies, surely they would be easy to sell or give away.
Female cockatiels are rather dull compared to the male, so a true pair or two males would be better. Two female cockatiels may get a bit sassy in Spring as they will see their aviary mate as a potential competition for a nesting hole, whether you put a breeding box in not. Two cocks get on better together.
The conures are harder(impossible) to sex but easy with dna testing.
All the long-tailed parrots (parakeets) require a long flight rather than a roomy one. It is better to have a 3 or better even 4m long flight with good weather protection on the northern side. The 2m height is ok and the 2m width could easily be divided into two 1m wide flights if the birds get too bossy.
Don't worry about the 'don't like birds in cages' brigade. Common aviary birds are bred in captivity, and are used to being confined providing they have good room to stretch their wings.
In fact, breeders of the rarer species are helping the endangered wild species by providing their young to the market so wild-caught/smuggling birds will become uneconomical.
The square one you propose is suited for canaries/finches and if you insist on parrots, maybe a colony of fishers lovebirds or some of the small parrotlets.