Are DropBox files viewed on iOS devices taking up space on them?

Yes. The files are cloud based until you favorite them.

Straight from DropBox:

How much can I store on my phone or tablet?

The Dropbox iPhone app can save as many files as your iPhone or iPod Touch can hold or Dropbox space allows. If you find yourself running out of space on your iPhone, removing files from your Favorites list will clear up space on your device. If you're running out of Dropbox space, you can delete files from your Dropbox, or you might want to consider upgrading to a bigger Dropbox.

I think they cache them locally cause sometimes I'm able to view the images in my folders even while I'm offline but those files aren't on my Favorites.

I contacted DropBox in relation to this. The files will only stay on the device itself in the sandbox area if they are favourited. If not, they will load into the memory and be dropped from memory once the application closes. Because they are cloud-based, they are "read" then "dropped" once no longer being "read". Kind of like a while loop in programming.

Source: DropBox technical support

If marked as favourite then on iPad/iPod/iPhone

Looking at file means that it is temporarily downloaded to view until application is closed, then it is removed.