So, yes the green algae is hair algae. It is common in new tanks and feeds mainly from stuff like phosphates and other things in the water column.
If you are feeding dry foods like flakes, pellets and the likes, maybe reduce a little the amount and it will help starving the algae. Also the best way to get rid of it is by having other types of algae competing for the same food. A refugium where you put macro algae is a great and simple way of achieving this. A refugium can be as simple as one of the partitions in your sump with a light over it (preferably on the 6500 K coloration, and the bulb and fixture can be bought for cheap at Home Depot Lowes), a bucket, a 10 gal tank, etc..
The little green balls, is also an algae called valonia, also called bubble algae. some crabs eat them
The brown spots do look like diatoms. Diatoms do go away with time, as they are very common while the tank is cyling and during the first few months afterwards.
In a nutshell, what is going on is normal and expected :-)
JM