Cycling issues

Hi all! It’s been 8 years since my last post! Wow. Anyway, I am cycling/reviving a 10 gallon nano tank (reef) and I noticed that when the ammonia spiked so did the nitrates and the nitrites. But now, the ammonia remains basically the same (0.5ppm), while my nitrites are zero and nitrates are steadily increasing. Obviously, when I previously retired that same tank, there was die off in the live rock. However, I am just curious as to why it seems to skip over the nitrites entirely in the cycle. Is it just that nitrites are converted so quickly to nitrates? It has been cycling for about three weeks now. Why is there still ammonia in my tank? The die off? In my experience, I never saw ammonia while cycling after at most the first week. Would some chaeto maybe help?

Thanks,

Lukas