HOW TO CREATE A REPEATING LOGO PATTERN-BACKGROUND

What kind of repeating pattern do you want? If you just need to tile an image you could print it to pdf and save the pdf as jpeg to a folder, for example:

Or arrange multiple copies of your image on a Light Table and print the Light Table to pdf as jpg.

You can't. That's not what Aperture is for.

Why not use Photoshop CC to create it? Or Acorn or Pixelmator or any other "image" editor. Aperture is a *photo* editor which is very different. It is a product for photographers.