Sind „Annetaan“-Artikel also dazu gedacht, verschenkt zu werden?

Yes

Yes! Though I suggest reading description carefully to make sure.

Yes, many people want to give stuff away because there is an expectation that who ever gets it also organizes transport. So it is easier for them.

Indeed, it does. Instead of pestering the person giving you stuff to carry it, bring it here or there, or transport it for you, I advise you to make your own arrangements. Also, giving a pack of coffee (if you can) in return, even when it is not requested, will go a long way! I have told people who have asked the same question this.

Sometimes a courtesy packet of coffee is expected, but other than that for free, yes.