Can I connect a keyboard via micro-usb to a smartphone which doesn't support OTG? My phone has no OTG support. A standard USB keyboard connected using an OTG cable doesn't work or even get recognized. Would a keyboard which instead connects via micro-usb work? Or would the phone require OTG support for that too?

The version of Android is 5.1.1. The phone is not rooted.
A keyboard with micro-USB connector is simply the combination of a keyboard with an OTG adapter, therefore this will not help you if your device has no USB OTG support. 

If you want to connect a keyboard to your Android phone instead you may try to use a Bluetooth keyboard.