Is there a way to set an event handler without doing it manually in the classname.designer.cs file other than double-clicking the UI element?
Click on the lightning bolt icon in the Properties window. Double click on the event you want to implement.
If I am following your question correctly, you can simply do it in your code like this:
myButton.Click += myHandler;
Or you can use an anonymous delegate:
myButton.Click += delegate { MessageBox.Show("Clicked!"); };
Sure. Use myControl.Event += new EventHandler(SomeHandlerMethodInYourClass) somewhere during initialization eg. in the form constructor.
myControl.Event += new EventHandler(SomeHandlerMethodInYourClass)