2. to study its consequences i.e. study it as independent variable for some important outcome
3. To study its determinants
4. to study mediating role of different variables
5. to study moderating role of different variable
I suggest this order. Study the literature to find the gap. I believe that one can find vast literature on determinants and consequences of dividend policy. Try to find some variables that moderate to its determinants or consequences. For instance, Fuller (2010) found that high quality, low quality and medium quality firms may use dividends differently.
See the interesting article
Fuller, K. and Blau, B.M. (2010), “Signaling, Free Cash Flow and ‘Nonmonotonic’ Dividends”, Financial Review, Vol. 45 No. 1, pp. 21–56.
Dividend policy is perfectly mixed with corporate governance related issues. Browse the thematical collections of free papers on corporate governance at our web-site https://www.virtusinterpress.org/A-set-of-updated-thematic-paper-collections-from-Virtus-Interpress.html to find more than 30 thematical collections. There is a great variety of topics.
In terms of dividend policy, I propose the following research topic: Analysis of changes in the significance level of key determinants of paying or not paying dividends correlated with the change in the economic situation, changes in the development strategy, changes in the company's mission, restructuring, making decisions on new investment projects, etc.