In each case, you need to verify that your ideas are novel and useful in the context of their own fields, and express them in the languages of those fields. It may be better, rather than going independent, to explain the situation to your advisor, and ask for recommendations and introductions to researchers in the relevant areas.
I have some experience of the patent process, fortunately as an employee with my employer paying all the costs. It has its own language. Converting an idea to a properly constructed series of claims is a specialized skill. I have had trouble reviewing a patent application to check that it correctly reflected an invention I completely understood. I have no idea how much it costs to get a patent written up and filed, but it is definitely not free.
If the original work were done "on the job" as a supported researcher, you need to check into the university's intellectual property rules and your own contracts.