Nonononono, you cannot have twice as many fish. Stop listening to the shop guy, he may be keen but he's wrong.
I've had a google and the Aqua Flow looks like a fairly basic internal filter- nothing wrong with it, no bells and whistles but it will do the job in a well stocked tank. It may be on the small side for your tank so an upgrade would help.
The bottom part you are replacing every month is activated carbon. It's not completely necessary to use it if the water quality is OK. It's expensive to keep replacing, so a lot of fishkeepers don't bother with it at all and just stick to normal sponges. If you do want to continue using it then replace it every month like you are doing.
You will need to rinse out the other filter sponge with water taken from the tank. Do NOT use tap water to clean the sponges, that will kill off all the good bacteria and your water quality will take a nosedive.
You'll need a water test kit to monitor the water quality. Something like this (shop around, you might find it cheaper) will do what you need.
This explains what you need to know about the nitrogen cycle. How long did your fishless cycle take?
The algae is probably down to the water. If you test then you'll know what's going on. You may need to do a phosphate test as well which the mini test kit doesn't test for, but a good aquatic store should be able to test it for you.