How to detect if a person is interacting (as in touching) some object in an image?
There are papers that show how to estimate different poses. For example this one gives an overview of different methods: PoseTrack: A Benchmark for Human Pose Estimation and Tracking. You can take this benchmark and group all the poses into needed categories. For example, by manually assigning your groups. And then you use the categorization of poses like in paper and convert to the poses you need.

One of the solutions for pose tracking is Mask R-CNN. It uses a neural network with convolutional layers and predicts in parallel class, box and binary mask. Here is the original Mask R-CNN paper. And here is the ProTracker algorithm that achieved one of the best results on PoseTrack.