“his sister said to Pharaoh’s daughter.” Moses’ sister Miriam was able to approach Pharaoh’s daughter. The Bible does not say why; it is possible that it was due to Miriam’s young age, and/or to God acting in the situation.
“Should I go and call a nurse for you from the Hebrew women.” This would not have seemed strange to Pharaoh’s daughter because many women had had their baby boys killed due to Pharaoh’s decree to kill the male babies, so many women would have been producing milk but not had babies to feed.