Can you use a microscope without an eyepiece?
Yes, you can. I have a microscope where the data can be transferred to a screen on a computer instead of going to the eyepiece. This microscope has both an eyepiece and the option to redirect the image to a screen. However, I also have a microscope with a screen only. So, I suppose you can have a microscope without an eyepiece.

I have never come across a microscope that has neither an eyepiece nor a camera but I don't know whether it's possible or not.