There is “R” shortcut for Arm record (Record Enable), and “*” (star on the Pad) shortcut for Record from the Transport panel, as default settings.
If you want to check your Key Commands settings, choose File > Key Commands menu. Here, you can insert (write) any function in to the search field. Then click to glass with + button, Cubase will find other Key commands for this word.
No, it’s not truth, you have to undo the Record Ready button , for playback. Probably, you are mistaken this with Monitor button. This looks like speaker, if it’s on, it is orange. If this is on (is orange), you can listen the signal from the input of your audio device, not from the tracks. If it’s off (grey), you can listen the track, not the input.