I have a ceiling fan in a screened in porch. I would like to install a security camera on the outside of the porch's soffit. Can I connect either a USB cable or a 110 electrical wire from the ceiling fan box to the security camera? The ceiling fan is not on a switch.
A little unusual (but not impossible) to have a ceiling fan not on a switch at all. But if that is the case then you definitely have always hot in the fan box. If there really is a switch somewhere then you may have always hot in the fan box, or you may only have switched hot. Of course, if there is a switch and only switched hot in the fan box, but that switch never gets turned off because nobody knows where it is, then you have a practical always hot anyway.
You can't run USB or any low voltage into the fan box. You can splice into hot and neutral in the box and run that to another box and install a receptacle in that box, either with a USB port built in (costs a little more, but one less exposed gadget) or plug in a standard USB adapter.
Depending on the type of ceiling and how far away the camera will be from the fan, you can either run non-metallic cable (a.k.a. Romex) through the ceiling or you can use conduit, Legrand Wiremold or similar products on the surface.