Data Science Career: From Researcher To Data Scientist
Great question! I can appreciate that you have a base of statistics to work from. Most data scientists - especially the ones that go to these data "camps" or whatever - out there do not have this and it should serve you well in your career. Here are some answers to your questions, in order:


Your background will help you because you are used to things like study design and execution and working with data. But I don't seen anything specific to HCI that would help you. When you are a good data scientist, the data itself takes on a muted importance. Right now, when I work on a project, I care that the data was collected in a sustainable way, but what the data is doesn't really matter. Eventually you will reach this too - it's all just numbers and math :-)
You have the statistics side. So now you need the (1) programming skills and the (2) the modeling skills. You should choose to learn a language like Python or R and develop your skills there. From there, you should start looking at the relevant libraries like Tensorflow and Keras to help you build your modeling skills. You should also pick up a textbook or some other resource that talks about what models actually do and how you can tune them, agnostic of the language you choose. Finally, you'll be ready for some research on neural networks and how those work. The measure of success here is being able to write some "traditional" models in Tensorflow (like regression, decision trees, etc) and also being able to write a neural network in Keras. 


I think that your base of already working around experiments and (presumably) applying the scientific method will serve you well and already puts you ahead of most data scientists out there. Now, it's just a matter of being able to do all of that with code and, if you follow the steps above, I think you will see those connections and how you can enter the world of data science.