In order to convince Anna to invite people in the Studio, you have to choose the Slut Route first. After that, progress with the Main Storyline until Anna has 4 or 5 Hearts and make sure you already completed her Inner Regret Questline.
As for your question about Charlotte, make sure you went to Charlotte's Yacht first and when you're given 2 dialogues indicating Charlotte's or Anna's Route, pick Anna's. Then continue visiting Charlotte until you're having a threesome with Charlotte and Anna on the Yacht. Only by then you can invite Charlotte to the Studio.