You can sex your spider from 5cm and up. but the smaller the spider the harder it is to sex as every thing is still small.
You need to get your self some kind of magnifying glass or microscope?.
Or take the molt to some one with the above equipment.
Then it is difficult to give a time? it could be 1year up to 2 years for a spider to mature, there is no fixed growth rate for tarantulas.
It also depends if you got a male and a female, the males tend to mature faster than the females do.
It depends on the species as well, like your Psalmopoeus species,the growth rate is fast and the males mature with in 18months.
Same for your H incei males the mature with in 1 year.