Could Persephone have kids in the myths? Or was she like Artemis, Hestia, etc.?

She had no children but it never says that she couldn't it's not like Artemis or Hera. In some stories she and Zeus are the parents of Zaegrus or Dionysius. In several stories she rasises Dionysius, and in many she gives some care to Adonis when he is young. In most stories Persephone is barren.

Yes, she actually has children. Melinoe is the child she bore Zeus after he tricked her by disguising himself as Hades. Or sometimes Melinoe is a child of Hades and Persephone.

Macaria (in one myth- in another she's a completely different person) is her second daughter, the goddess of a blessed after-life, daughter or her and Hades.