Last January (2016), the inheritance feature was reworked to rationalize how to create relationships between sites.
Everything is now configurable directly in the settings of the parent website (in the "Instance" menu of the settings) - that’s because parents make the rules.

This is pretty straightforward. The first option defines upwards searchability (many to one), the second one downwards searchability (one to many), and the third one encourages children to share their toys among them.

Content inheritance
Let us be precise: this does not, at any level, create copies of content. If I write a news article and publish it on my website, it will appear in the search results of another website if inheritance is activated between them, but clicking on it will redirect to my website.
In other words, content does not appear in the list of contents, in the administration panel of other websites.

Visibility management is a no-brainer. I will see the inherited content if and only if I am authorized on the target content (and implicitly on the target website).
Everything is Google authenticated.

Groups and metadata inheritance
Those two entities, while never appearing in search results for obvious reasons (they are settings on rather than of content), can be shared among different sites.
In this case, you define platform-wide groups and metadata values, rather than site-only.
Be aware, however, that platform groups become available for every single site within the platform.