How are some people able to continue growing after reaching maturity?
Usually the cause is 'acromegaly' but there are numerous possible causes.

It is impossible to start growing in length after your bones have matured too much. This is because of the 'Epiphyseal plate' this is a anatomical structure in bones that is necessary for length growth in bones and it degenerates at the start of adulthood.

The most common cause, although still not a common disease, for gigantism is acromegalia. It's cause is an abnormally high amount of growth hormone in the body which is most commonly caused by a hormone secreting tumor.

When the onset of this disease happens before the epiphyseal plates have degenerated it can cause them to stay active in which case the patient will continue growing.

Note: When the onset is after the degeneration of the disks it doesn't cause gigantism but it still causes a very recognizable change in appearance and the model for Shrek in the movie suffered from this illness.

Edit: Sorry, I didn't notice your subquestions initially. Yes, another possible cause in men is the lack of testosterone because this hormone is normally responsible for the degeneration of the plates in men.

Edit 2: In women estrogen is the hormone that is responsible for this, which explains why the length of men and women isn't dependent on testosterone in both cases