For Backdrop are there any themes with slideshow or carousel function built in, as there are for Drupal?
I don't think that there is any such theme at this time. Here is a recent spreadsheet I created of all the themes currently available.
There are modules that provide pretty easy slideshow support, such that I do not think you need slideshow support in your theme.
I'm working on a new contrib theme (Tatsu) and would consider providing some support for slideshows or carousels, if I can determine exactly what that means in Backdrop land. I created an issue for Tatsu here, please feel free to comment:
Do you have the time/skills to create a sub-theme or are you looking for something that will work 100% out of the box?