I don't think that you will learn much about data science (meaning, acquire understanding and skills) by using software tools like Tableau. Such tools are targeting mainly advanced users (not data scientists), for example analysts and other subject matter experts, who use graphical user interface (GUI) to analyze and (mostly) visualize data. Having said that, software tools like Tableau might be good enough to perform initial phase of data science workflow: exploratory data analysis (EDA).
In terms of data science self-education, there are several popular online courses (MOOCs) that you can choose from (most come in both free and paid versions). In addition to the one on Udacity that you've mentioned (https://www.udacity.com/course/ud359), there are two data science courses on Coursera: Introduction to Data Science by University of Washington (https://www.coursera.org/course/datasci) and a set of courses from Data Science specialization by Johns Hopkins University (https://www.coursera.org/specialization/jhudatascience/1). Note that you can take specialization's individual courses for free at your convenience. There are several other, albeit less popular, data science MOOCs.
In terms of data sources, I'm not sure what do you mean by "Dummy Data", but there is a wealth of open data sets, including many in the area of public health. You can review corresponding resources, listed on KDnuggets (http://www.kdnuggets.com/datasets/index.html) and choose ones that you're interested in. For a country-level analysis, the fastest way to obtain data is finding and visiting corresponding open data government websites. For example, for public health data in US, I would go to http://www.healthdata.gov and http://www.data.gov (the latter - for corresponding non-medical data that you might want to include in your analysis).
In regard to research papers in the area of public health, I have two comments: 1) most empirical research in that (or any other) area IMHO can be considered a data science study/project; 2) you need to perform a literature review in the area or on the topic of your interest, so you're on your own in that sense.
Finally, a note on software tools. If you're serious about data science, I would suggest to invest some time in learning either R, or Python (if you don't know them already), as those are two most popular open source tools among data scientists nowadays. Both have a variety of feature-rich development environments as well as large ecosystems of packages/libraries and users/developers all over the world.
You might also find useful some of my other related answers here on Data Science StackExchange site. For example, I recommend you to read this answer, this answer and this answer. Good luck!