Do photos in a Series show up on my profile?

Yes. The photos in a Series appear on your profile feed, in chronological order like any other photo. They also appear in Camera, Lens, and Category feeds where they apply.

The Series itself, and its photo overlay, don't appear in your profile feed. You can find the Series under the Series tab on your profile, where it has its own page. Removing a photo from a Series, or deleting the Series, doesn't remove the photo from your profile.

See How will a Series look on my profile or in other feeds? and Can I remove or reorder photos in a Series?.