#1 Does this work with a vga to hdmi adapter? i need to connect this to a windows pc
As long as the adapters work as intended then you should not run into any issues. You simply want to ensure the adapter you get is to convert VGA to HDMI not the other way.
#2 How to adjust the vertical shift? The picture is on my ceiling and I need the lens to shift down vertically.
Use the settings or like I did I had to flip the projector upside down and then go to settings and flip the image