Is there a feature like the Format Painter of Microsoft Word?

A tool like that is already there on the Editor but works in a different way. It is called Pick and Apply format. You will find two different buttons on the editor toolbar, one to pick a format and other to apply it. This way, you can pick a format from some selected text and go on applying this format to another selected text. The picked format is remembered for the session till you pick another format.

There is also a feature to include the paragraph properties in the picked format. But you have to put on that option. It is off by default. You will find it in the General Options–Editor.