When adjusting the handles of an anchor point, how can I adjust both handles to an equal length or adjust them both at the same time?
As @llan answered, you can use the Convert Anchor Tool to click-drag two symmetrical handles out from an anchor point.
If you already have two non-symmetrical handles, or just one handle and want a second one, Illustrator provides no method to easily match two (or more) non-symmetrical handles other than this click-drag option of the Convert Anchor Tool.
In other words, no. You can’t really alter two handles simultaneously unless they are smooth point handles.