Yes, by using a Retail Express package you can set up a “pointer” to a real product with a different price. This new SKU will synchronise and allow you to have a discounted or free price. You can also use packages for “Bundles” the stock levels will update according to the components within the package.
Yes there is an option to do this, remember that it will also show products and publish them once stock is available, so you need to be aware that new products could go up before you are ready.
Please make sure the product has Export to Web selected, a Sales Channel and Source Group assigned. Also make sure the product is not disabled.