Magento – How and where to change add to cart message in Magento 2

By default in Magento, if you go to System -> Configuration -> Catalog -> Inventory and set Backorders to "Allow Qty Below 0", and on the product page in the inventory tab you have the following settings:

then, the product should show as "In stock" on frontend and the customer should be able to add it to cart:

By changing the Stock Availability of the product to "Out of stock" you should be able to get it to show as "Out of stock" on the frontend:

Are you trying this with the default Magento theme? If you are using a custom theme and this is not happening for you with these setting there might be a problem in the theme you are using.

You can change message from code in cartController. Extend cartController into your local. In cartController find below code:

if (!$cart->getQuote()->getHasError()) {
            $message = $this->__('%s was added to your shopping cart.', Mage::helper('core')->escapeHtml($product->getName()));
            $this->_getSession()->addSuccess($message);
}

and change message. And if you want to redirect to same product page then system >> configuration >> sales >> checkout Expand "shopping cart" tab and set "NO" to "After Adding a Product Redirect to Shopping Cart".