Thank you for posting those test results, it's help us better advise you
Something is definitely off here, but before we all overreact, let's consider a few things first:
Let's start with this statement: There is no way your tank should not be cycled after running for 9 weeks, if you added the proper amount of ammonia and bacteria initially. A brand new tank with totally sterile rock and sand will cycle in 3 to 4 weeks tops. It's a biological process, and quite predictable.
What I see in your test results is the ammonia at about 0.50 ppm, with elevated nitrite, and low nitrate (allow me to explain). This makes me think that the tank was not set up to cycle with the correct amount of bacteria and ammonia going back those 9 weeks ago. Rather, either ammonia must have been added more recently, or bacteria would have been added more recently. I believe this is what got your cycle going, and resulted in the nitrite you are seeing now. I don't think there's any other explanation given the time line you're mentioned.
Right now, you have bacteria converting ammonia to nitrite, which is great. However, nitrite present in the water will cause an artificially high result for nitrate. For this reason, you cannot accurately test your nitrate concentration when you have nitrite present. At this point, there's no reason to think you're nitrate is high.
Here's what I would suggest going forward: Let this ride. I don't know what happened 9 weeks ago, but right now your tank is maybe a few days to a week or so from completing its cycle. Don't do water changes, let the ammonia fall to 0.25 ppm or less on your ATI test kit, and proceed to either slowly stock your tank with some hardy fish, or take some time to address the algae you're seeing. But once that ammonia drops to 0.25 ppm or less, you're cycled
A couple more thoughts that I hope will help:
It's not a bad idea to turn your lights off during this period to keep that algae down. Turn them on once you add (desirable) photosynthetic organisms.
At least for now, stop testing pH. pH will fluctuate in a cycling tank, and many long-term successful reefers don't test pH at all. Unless you are growing corals professionally or competitively, you can skip pH testing.
Likewise, you can safely ditch the nitrite test altogether. Nitrite is totally non-toxic in marine aquaria, unlike in freshwater where it's toxic like ammonia. In saltwater systems there's no reason to test for or be concerned with nitrite at all. The only caveat is that, again, when nitrite is present it will cause your nitrate to look artificially high. For this reason I would not test or take action for nitrate until the nitrite has zeroed out. <<That would be the only, minor reason to test for nitrite for a marine tank, in my humble opinion
I hope this helps and please keep us posted on your progress!
