AIDA herself is in the framework, so she could easily knew the location of Patriot (i.e. the SHIELD HQ; since she'd been there for a long time). But we have seen Fitz asking the location from Daisy. However, she might not know it's that location that is being used.
At 35:11- Ward could easily kill both Aida and Fitz but doesn't do it. However, moments ago Jemma was pleading him not to act.