How to start my own research?
Specialize, focus and diversify your research agenda solely on 2-3 open questions/problems the next years. There is not really another path. Especially in fundamental sciences it's hard to plan an academic career, so you have to take risks, therefore diversify them. And this is also encouraged by the academic system to achieve results beyond the state of the art and knowledge. With many publications you might get a staff position, but to get tenure as a professor you need to become one of the few experts in your field for a distinct method or sub-topic. But don't understand this as a 2nd PhD, it's now your duty to acquire funding, PhD students and build a scientific network around you. You need to acquire people now that work with or for you. You showed with your PhD that you can work alone on a scientific question, for tenure you need show that you can set up aresearch agenda for younger scientists and bigger projects with several partners and that you are able to manage successfully and financially projects aparat from teaching duties. You also have to show autonomy, staying with your supervisor your whole post-doc time is disadvantegous.