ah, in those cases you have to press F5 to unstuck things (pretty useful button) or just pressing the RMB outside the menu.
Also, the only way to have a fapet following you is either canceling sex or using the Call Command (you get it after processing in the story) So take that in mind when you need to do a Bring X fapet Quest.
PD: the only indication about a Fapet following you, is a yellow circle with numbers under your HUD