1. There are absolutely animals that can be domesticated. Including cats. Cats are a multiversal constant. If you would like Era to procure a cat, you may do so! Note there are several breeds "imported" from other worlds as well as native strains, the latter being somewhat less docile. However, they have already begun to interbreed.

2. More information on canon updates is here, which does not make note of a dream mechanism best I can tell! Era can certainly obtain new equipment (and her underwater breathing ability) by revisiting her homeworld for a canon update. Aside from that, can you clarify your question based on that page? Thanks!