This plant with many green leaves has now produced, at the very top, a small bunch of yellow round pods (looks like buttons).

[b]TWO[/b] questions: Is the plant flowering? + Can I harvest these yellow things as seeds for next year?

Yes, that's the tansy flower. I never deliberately planted any seeds, but my tansy was so invasive - whether from seeds or roots I don't know - that I ended yanking it all up.