Question

I see all the feed_* methods are deprecated… (I am using version 3.0.2).
What replaces them? How do I publish something to the user’s feed.

Answer 1

This answer is not about the Java API in particular, but it might still be useful:

We want to remind you that starting on that day, the only way to publish Feed stories into the stream will be via the stream publishing methods (stream.publish, FB.Connect.streamPublish, and Facebook.streamPublish). Posts published using the stream publishing methods contain only structured plain text data, which makes them easier to render on a variety of devices, including mobile phones and gaming consoles.

and

We will still publish stories when you call users.setStatus and status.set, but we encourage all developers to migrate to the stream publishing methods, as they let you set a user’s status easily.
Read more detail about these changes on the Stream page of our Developer Roadmap.

(both from a mail to Facebook application developers)

So you should probably look for methods starting with stream_* rather than feed_*