Resnet with only one output. Classification or Regression?

Hi, first post here at the forums. I am a beginner at deep learning, still watching the videos from 2018 course (currently in lesson 3), but I am really enjoying it.

I am struggling with some concepts about Resnet and similar networks. I see that they are used mostly for classification tasks, but some applications like Open NSFW from Yahoo (which is based on Resnet) has only one output like, in this example, the NSFW Score.

I imagine that is easy to get most of the answers by inspecting the caffe model from Open NSFW, but I don’t have the knowledge to do that.

So, here go my questions
’1) Is Open NSFW and similar applications still a classification task? Or is a regression task, even if it is based on pre-trained classification network?

Regarding the adaptation of Resnet/Vgg/etc to this kind of task
’2) Is it necessary to change the last layer or add a new last layer? What is the difference between these layers.
'3) How to label my dataset? It is simply safe_for_work and non_safe_for_work labels (similar to dogs vs cats) and the NSFW score is just the probability of the latter category (the former category is just ignored)? Or the dataset need to be labeled by degrees of how safe for work each picture is, and in this case, the NSFW score is an attempt to predict this?

Thank you in advance and sorry for my odd english (non-native speaker)