Wear clothes - I know that hermit crabs wear shells

Make music - I know that birds sing, and a quick Google search shows whales and seals seem to make "music" as well

Theorize - Depending on what you mean of course (but I agree with you about e.g. scientific hypotheses to be tested), but as an example apparently birds "theorize about the minds of others", again by Google search

Writing - Definitely a stretch here (and so I agree with you) but animals do leave chemical markings for others