> Do these definitions work for everyone?

They're fine for me, but my qualms with the word "religion" is mostly in general implication rather than a definition established for any particular discussion.

My qualm with the word (and that of many like-minded Christians; it's a qualm I see a lot of others having) is that it implies ritual, whether organized or not. The contrasting word would be "relationship," as in, "Christianity is a relationship not a religion." "Relationship" implies a lot more of what's involved: communication, love, service, and so forth, just as with human relationships. It implies something that involves the entirety of what we are, rather than one of many separable aspects. It implies that it's personal, instead of just a belief or habit or cultural background.

But as long as that's understood, I don't care if the word "religion" is used to describe it.