I can add rows conveniently using Option+Shift+Up Arrow (insert above) or Option+Shift+Down Arrow(insert below).
Is there a keyboard shortcut to delete the current row?
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With Numbers 11 and earlier, by default, no, there's no shortcut.
You can create one yourself though:
Open System Preferences → Keyboard → Shortcuts → App Shortcuts.
Click the + button to add a new shortcut.
Set the Application to Numbers.app, and the Menu Title to Delete Row.
Set your keyboard shortcut and press Add.