How to check if sudo password has been entered for this terminal session?

You can use:

if sudo -n true 2>/dev/null; then 
    echo "I got sudo"
else
    echo "I don't have sudo"
fi

The -n (non-interactive) option prevents sudo from prompting the user for a password. If a password is required for the command to run, sudo will display an error message (redirected to /dev/null) and exit. If the password is not required, then this expression is true: sudo -n true 2>/dev/null.