Hi thanks for those tests. Can you also let me know what your temp, salinity, and pH are?
Based on the two tests you showed, you are definitely very high on PO4. Your NO3 appears to be fine. However, please keep in mind that the API test kits are really terrible. With a small setup like yours and being relatively new to the hobby, I'm not suggesting that you invest in high end test kits. Just realize that API test will give you limited info. With an API test for PO4, you should be aiming for it to be 0ppm. In reality, you want PO4 to be around 0.1 - 0.05 ppm (depends whom you ask), but you can't measure that low with API. For nitrate, having around 5ppm is fine in my opinion, although some would suggest higher (20ppm or greater). Both of these nutrients are needed for coral growth---but algae also feeds on them, so it's a constant tug-of-war to figure out the best combo of those values for YOUR tank.
In this case, with all that algae, it can be hard to determine what the true value of your nutrients would usually be based on your standard tank care regimen. This is because the algae is busy consuming your nutrients so the so-called "true" levels are probably much higher.
Given the age of your tank, you should definitely be going through the ugly stages now. That's the nasty period that your water chemistry/ecosystem is settling out. That being said, you do have too much algae now. Best course for your particular tank (I'm assuming you don't have a skimmer or other waste export method, right?) would be to do regular 15% twice a week for a while. After a month of this, the algae should be pretty much gone and your API phosphate should show zero. Once the algae is under control, you can go down to one 15% water change once a week. There are additives and other things you can do to control algae, but I wouldn't recommend that in your setup. Just plain old water changes should work wonders. You can scrub your rocks with a toothbrush before your water changes to dislodge algae too.
One important note: you don't want to aim for true zero nutrient levels in the water or you can risk a dino explosion. They thrive in super low nutrient system. Again, it'll be hard to tell that with PO4 using API...but if you keep your NO3 around 5ppm or so by API and are doing water changes as suggested, then you can assume that you have enough trace PO4 around too.
