Q.About sunflowers
I have a sunflower my boyfriend bought me that was already in a pot and now it is dying off. I’m wondering if I should plant it because I want it to come back next year, or is that a bad idea seeing as summer is now over. What do I do with it over winter? I don’t have a garden, so what should my soil be like if I do plant it? Should I dig up all the roots in the soil? Get all the rocks out??

Your plant may be an annual or a perennial. Annuals will only live one season and should be thrown away after blooming.
If you have a perennial you can plant into the ground. If you have the tag that came with the plant it should say which type of plant you have.
If you don't have a tag, it is difficult to say which type of plant you have.
Here is a link that may have more help.