Trouble with fishless cycling: no ammonia, high nitrites/nitrates
you are aware how the nitrogen cycle works??
Waste breaks down into ammonia, then one bacteria converts that to nitrites. then another bacteria then converts that to nitrates.
from what you've described, the first bacteria is thriving converting all the ammonia in nitrites. though the second isn't as established yet.
your algae problem is a side effect of your original problem as its using the nitrogen to grow.
so to start with don't worry about water changes. the bacteria needs to consume the nitrites to grow and colonize your tank. having nitrates is fine, that isn't going anywhere. when you have fish in the tank to minamize the amount of nitrates we do water changes. my tanks are usally around 4ppm.
if you are still adding more ammonia, i would stop. keep waiting and testing till you get 0 nitrites. you can then do a water change to bring down your nirates to acceptable levels.
I've never had a serious algae problem. but basic science tells me plants need light, nutrients and water to grow. so if you cover your tank up with a dark towel your algae should die off... check the forum there is bound to be a ton of posts on algae removal.