User Control - Custom Properties

You do this via attributes on the properties, like this:

[Description("Test text displayed in the textbox"),Category("Data")] 
public string Text {
  get => myInnerTextBox.Text;
  set => myInnerTextBox.Text = value;
}

The category is the heading under which the property will appear in the Visual Studio Properties box. Here's a more complete MSDN reference, including a list of categories.

It is very simple, just add a property:

public string Value {
  get { return textBox1.Text; }
  set { textBox1.Text = value; }
}

Using the Text property is a bit trickier, the UserControl class intentionally hides it. You'll need to override the attributes to put it back in working order:

[Browsable(true), EditorBrowsable(EditorBrowsableState.Always), Bindable(true)]
[DesignerSerializationVisibility(DesignerSerializationVisibility.Visible)]
public override string Text {
  get { return textBox1.Text; }
  set { textBox1.Text = value; }
}

Just add public properties to the user control.

You can add [Category("MyCategory")] and [Description("A property that controls the wossname")] attributes to make it nicer, but as long as it's a public property it should show up in the property panel.