I just got my Pi Zero and I am going through the setup process with the mouse which is working fine but then when I switch over to my keyboard it doesn't work at all. I am using an iPad wall adapter to power the pi and the USB converter that I added to my order of the Pi. What is causing the keyboard to not but the mouse is?
The USB port on the Pi Zero tends to supply less power than that of a full Pi--regardless of how you are powering the Pi Zero--so expect compatibility with fewer USB devices. One way to get around common USB power issues is to connect through an externally powered USB hub.
That failing, with a serial debug console run
dmesg and see if there are any errors preventing the keyboard from enumerating properly.
I've had the same experience with the Zero. It's easy to overload it, causing it to reboot.
You can use a powered hub, as suggested. Another option is to connect the Zero to the local network, then log into it from another machine.
The Zero has its place, but cannot really run a desktop environment at normal desktop resolutions very well.