Sliders width doesn't seem to include the input box about egui HOT 2 CLOSED

This is definitely because of ui.columns, since that function does not allow the containing UI to properly expand to fit the contents of the columns. I should fix this or deprecate the function in the next version of Egui.

As for the overlap in your second example code. Try setting some min/max widths of the columns:

ui.horizontal(|ui| {
    ui.vertical(|ui| {
        ui.set_max_width(300.0);
        first_column(ui);
    });
    ui.serparator();
    ui.vertical(|ui| {
        ui.set_min_width(200.0);
        first_column(ui);
    });
    ...
});

from egui.

It may be because of using the columns() api to lay out the above window. Using this method I get a different result:

ui.horizontal(|ui|{
    ui.vertical(|ui| first_column(ui));
    ui.separator();
    ui.vertical(|ui| second_column(ui));
    ...
});

All elements are visible, but it adds some overlap:

from egui.