Yep, unfortunately, even 6 hatchets would be bullied if kept with angels and you can't realy keep 6 of them in the 15 gallon either. Idealy, re-home the hatchet you have. Having said that, if your angels don't pair up and you have a big group, they may be ok. the thing is, there's no way of knowing whether the angels will pair up and the hatchet on its own as things stand won't do all that well. Like I said, your best bet would be to find a new home for it, give it back to your LFS or buy another tank
If you are deffinate the gouramies are honeys, they should be ok in the 15 gallon. How well they get along will, however, depend on their sex and how well-planted/decorated the tank is. To sex them, males are more stream-lined than females and have generaly longer fins. the females are deeper-bodied, wider when viewed from above and should have an obvious bump when mature (due to being full of eggs (gravid)). Having said that, most people sex them based on color as males are brighter than females and develop a blue-black throat/underside color when in rbeeding condition. Unfortunately, some color morphs don't display this as readily and juveniles are difficult to sex based on color as all are generaly a dull brown color 9or red-orange for certain color morphs) with a horizontal stripe running along their bodies all of which are typical of a female. Do you have a picture of them all by any chance? They won't do well with adult angels and will want the top layers of the 15 gallon to themselves (which is another good reason to find the hatchet a new home).
About the requirements of gouramies - honeys are ok with about 5 gallons each but males are still territorial so putting them all, together, in a 15 gallon is pushing it slightly. I think they should be ok though as long as they have the top of the tank mainly to themselves and as long as they have plenty of hiding places and, especialy, floating plants (gets some if you don't already - even fake will do or very tall rooted ones). Larger gouramies vary rgeatly as far as volume requirements go. Keep in mind that 'gouramies' encompass a huge group of fish - people keep bettas in tanks as small as half a gallon (though I'd say 2.5-5 is more suitable) while the larger gouramies, like the osphronemus gourami, grow to 30" so require, obviously, huge tanks. It's impossible to generalise and say that all gouramies require 10-20 gallons. Having said that, most commonly available medium-sized gouramies have a minnimum tank size requirement of 20 gallons over-all but need at least 10 gallons per fish.
The angels won't necessarily pair as you have no way of telling whether they are male or female. As for whether they have reached sexual maturity, my experience with this fish is very limmited and what I do know just confuses me more
I realy doubt there's an accurate way of determining whether they have or have not but, if they are around 4", I would think they are, at least, getting there.
Don't worry about being confused
You'll get the hang of it gradualy. the key is to research every fish you plan to get long before you buy it and make sure you know as much as possible about it and it's requirements and can meet them. You'll be fine - you have a while to sort everything out now anyway as the only real problem you have is if those angels pair up.