Yes so far all my connections with apps work. I have iphone and i use the hdmi iphone adapter and am able to play. Hulu, disney+, youtube, netflix and even an anime app i use. This projector is the best one ive used. Only sucky part is if you have kids: they will guarentee take this from you and perminatly set it up in their room 

Yes, it will fit any Sony e mount body, either full frame (a7..., a9...), or aps-c (like a6500, etc) 

Yes and no. Using motion detection it doesn't work through a window. However.... using the timer inside it you can record through a window using it. How? Set the timer to record 4 minutes every 5 minutes for 1-5 hours or whatever time you need it to record for. This is what I do- just make sure you have a SD card with enough memory for the videos- I use a 32 GB SD card, I use it though a window as a security camera for my car....I live in an apartment so I can't hard wire anything and this works great for what it is. 

No 

yes, i had no problems with infinity focus with this adapter. the only FD mount lens i use anymore with my sony is a vivitar 20mm, and i pretty much only shoot infinity focus with it.