Do I have to cut back my sunflowers after flowering or do I even have to seed them annually anyway?
The sunflower is an annual flower. You can harvest and use the seeds from your own plant but you have to sow them every year.
The shrub sunflower (Topinambur; Latin name: H. tuberosus) is a perennial flower which lasts more than a year. However, it does not bloom as nicely as the annual sunflower.