Cursor moving broken except simple left and right

• iTerm2 version: 3.3.7
• OS version: MacOS 10.15.3
• Attach com.googlecode.iterm2.plisthere (drag-drop from finder into this window)

zsh is supposed to improve my shell experience. Currently, I see no benefit in using zsh except the cursor moving is bugged as follows:

Pressing HOME/POS1 key is supposed to move the cursor to the beginning of the line. Actual behaviour: nothing happens Same for END key.

Wordwise left and right moving doesnt work either: OPTION+left (or right) Actual behaviour: [D or [C get appended to the line instead of moving the cursor.

Also alternative home/end doesn't work: CNTRL+left (or right) Actual behaviour: nothing happens.

How to fix this and why this happens at all, it supposed to be a basic, reliable feature that shouldn't be not working in some setups.