Can I use MultilingualPress in a single-site WordPress installation?

You cannot use MultilingualPress in a single-site WordPress installation. For MultilingualPress you need to have a WordPress multisite installation.

Explanation in Detail: Why you can use MultilingualPress only in a WordPress multisite installation

To enable the use of MultilingualPress for a single site, we would have to interfere with the way WordPress saves content. However, there are plugins that accomplish exactly that. But we think this is a bad idea. After deactivating the plugin, you would lose access to your translated content.

The entire concept of MultilingualPress is based on using a corresponding site for each language (in the WordPress network, this means a multisite). Links between sites and between translated content (e.g. posts or terms) are saved in separate plugin tables. This makes it possible for the individual sites only to store the actual non-manipulated content, that is, without injected shortcode, as is (necessarily) the case for some single-site plugins.

If you currently have a single-site installation, you can change this to a multisite. You can find detailed instructions for this here.