yes algae will grow near the end of your cycle. It'll be there for a while. You can add a CUC now. You can do water changes too. It'll leave eventually on it's own.
Don't let nitrates get to 0. Same with phosphates. People tell you high nitrates and phosphates cause algae, but that's fine. 0 nitrates and 0 phosphates cause even bigger issues. SO if you have nitrates that are 5-10ppm and phosphates that are 0.03-0.1ppm, don't worry about them. The algae that grows can be eaten by snails.