It is impossible to answer this question without knowing more about what you want to find out, what the variables of interest are, what kinds of statistical techniques you are planning to use, what effect sizes you are expecting, etc.
Using multiple methods and multiple time points may be helpful but this also adds complications (e.g., how to integrate multiple sources of information in a statistical model; how to deal with potentially low convergent validity/agreement; how to model longitudinal data). Having more/multiple time points can compensate to a certain extent for a smaller sample, but again, the necessary/optimal sample size depends on multiple factors including the ones that I mentioned above.
Yes, it is possible, but you need to consider whether this is an optimal or feasible way to answer a research question. Perhaps you are looking at your research in the wrong way. It is sometimes better to start from the data you can access and work back to generating a viable research question.
I appreciate the honesty as I believe, in reflection, I am approaching this study the wrong way. I am too focused on the problem that 'needs to be addressed' rather than the accessible data. I will now go and review my approach to my next research study. Thank you for your time, everybody.
There is no problem with having multiple sources of data; in fact, that can strengthen your research. The key question is what you intend to accomplish with your research. With a small sample size, you are unlikely to be able to draw statistical conclusions. This sounds like a qualitative study more than a quantitative one. Qualitative studies can provide valuable insights, which later can be tested quantitatively. Your research potentially sounds very unstructured, but that depends on how you design the interview protocols and whether you impose a structure on how the diaries are to be maintained. A risk is that you may be getting very different data from each person, with results that aren't comparable.