For writers, is it normal to have periods where they don't feel like writing even if they love writing?

Absolutely. As a writer, I love to make stories and characters and worlds and make them come to life, but writing is hard. Its tiring and writers block often makes it really hard and tedious to keep going. I struggle a lot with losing motivation for my stories. Even when I have long times when I don’t work on a story, I still love writing and consider myself a writer.