How to get to Completer Popup on Down Arrow

[A Former User]

I've this subclass of QComboBox:

CustomCombo::CustomCombo(QStandardItemModel * model){
    completer = new QCompleter(this);
    proxy = new QSortFilterProxyModel(this);
    table = new QTableView(this);
    proxy->setSourceModel(model);
    proxy->setFilterKeyColumn(0);
    proxy->setFilterCaseSensitivity(Qt::CaseInsensitive);
    completer->setModel(proxy);
    completer->setPopup(table);
    completer->setWidget(this);
    completer->setCaseSensitivity(Qt::CaseInsensitive);

    //completer->setCompletionMode(QCompleter::UnfilteredPopupCompletion);
    table->horizontalHeader()->hide();
    table->verticalHeader()->hide();
    table->horizontalHeader()->setStretchLastSection(true);
    setModel(model);
    setContextMenuPolicy(Qt::NoContextMenu);
    setPlaceholderText("Select an Item");
    connect(this, &CustomCombo::currentTextChanged, [=]{proxy->setFilterFixedString(currentText());});
    connect(this, &CustomCombo::currentIndexChanged, [=]{setEditable(false);});
}
void CustomCombo::mousePressEvent(QMouseEvent *e){
    if(e->button() == Qt::RightButton){
        setEditable(true);
        setCompleter(completer);
        setCurrentText("");
    }
    QComboBox::mousePressEvent(e);
}
void CustomCombo::keyPressEvent(QKeyEvent *e){
    if(completer->popup()->isVisible() && e->key() == Qt::Key_Down)
        completer->popup()->setFocus(Qt::OtherFocusReason);
    else QComboBox::keyPressEvent(e);
}

and in the main window, I give it a model and add in layout like this:

Window::Window(QWidget *parent) : QWidget(parent){
    comboModel = new QStandardItemModel();
    comboModel->setColumnCount(2);
    for (int i = 0; i < 3; i++) {
        auto col1 = new QStandardItem("Left " + QString::number(i + 1));
        auto col2 = new QStandardItem("Right " + QString::number(i + 1));
        col2->setTextAlignment(Qt::AlignRight);
        comboModel->appendRow(QList<QStandardItem*>() << col1 << col2);

        col1 = new QStandardItem("Right " + QString::number(i + 1));
        col2 = new QStandardItem("Left " + QString::number(i + 1));
        col2->setTextAlignment(Qt::AlignRight);
        comboModel->appendRow(QList<QStandardItem*>() << col1 << col2);
    }
    auto lay = new QVBoxLayout(this);
    auto combo = new CustomCombo(comboModel);
    lay->addWidget(combo);
    lay->addStretch(1);
    setLayout(lay);
}

When I right click it clears the text and as I type in, it shows the matches. When I press down arrow, I want it to go to the popup and select items there instead of changing text in the box. Here's what it does on down arrow press:

One more thing, how to show both columns of the selected item in the combo box. Right now it shows only one column in the box. I can see other column only when popup opens. Something like this: