Keyboard shortcut for going onelevel up in midnight commander [mc]

If you go to Options->Panel-Options and tick the "Lynx-like motion" option you can use left-arrow to go to the parent directory and right-arrow to enter a directory.

Does Home, Enter count as a keyboard shortcut?

Short answer: No.

Longer answer: Ctrl + PageUp goes to the last diretory - not the parent, but this may be what you want in most cases. (https://www.midnight-commander.org/ticket/2420)

Without changing the default setup Alt + Y and Alt + U go to previous and next directory in history, which may be enough on most cases (Alt + H to see the full history). If not, you always have Home, Enter.

Alt + Arrows are used to move between windows on byobu/tmux.

To add a custom shortcut (like Backspace) to your user config:

echo 'CdParentSmart = backspace' >> ~/.config/mc/mc.keymap  # Globally in /etc/mc/mc.keymap

Here more related handy shortcuts.