Can I change or remove many products at once from the product list?

Yes. In Products → Manage Products, tick the products you want, or use the box in the header to select every product on the page. A bar appears at the bottom of the screen with these actions:

• Move to Draft: hides the selected products from your store without deleting them.
• Move to Trash: moves them to the product Trash. You can restore them from there later.
• Export: downloads the selected products as a CSV. This needs the Import/Export plugin.

Each button only shows if your staff role allows that action. There is no bulk publish button. To publish, open each product and change its status. To change prices in bulk, see the bulk price thread.