Hi! I saw nobody had replied to this yet.
From the pictures, looks like your ammonia is being turned into nitrites just fine, and you're getting low levels of nitrates already - so you're on the right path!
Once the nitrites go down as well your tank will be fully cycled.
I'm not sure why the levels would stay like this for weeks, though. Usually, once nitrites get converted into nitrates it's close to being done.
Do you add ammonia manually? (And if so, how much?) Do you have a running filter? Did any water changes in the meantime?