Mixed methods research is a methodology for conducting research that involves collecting, analysing and integrating quantitative and qualitative research.
I strongly recommend to combine qualitative and quantitative research methods and take into account "hybrid perspective". Such practice deepens our knowledge about analyzed issues and makes the research more comprehensive and complete. Actually it is advisable to make our research methods mixed. Sometimes the qualitative or quantitative perspective can be insufficient, hence it is possible to complement one method by another. Nevertheless, it seems that (in my opinion) there is a contractual limit when it comes to number of methods used in one research - "balance", exceeding witch causes the decrease of effectiveness (for instance too much data without context). Anyways, it depends on: 1) scale of the project, 2) population we want to test and the most important 3) issue we want to explain. I have also stared discussion on that subject and I'd love to invite you to join: https://www.researchgate.net/post/More_qualitatively_or_quantitatively_How_to_find_a_balance_in_various_research_methods_use
Yes, this is the underlying premise for mixed methods research. Mixed methods allows to gain a comprehensive understanding of any given phenomenon. Three core designs, convergent, sequential exploratory, and sequential explanatory, as outlined in Creswell & Plano-Clark, (2018) can be used depending upon the type of research question. However, it is important that not to use mixed methods merely to mix both qualitative and quantitative approaches. It is important to clearly justify the need for mixed methods and develop a clear mixed methods question. Integration of both qualitative and quantitative approaches is the key, at can occur at design, methods, analysis, and interpretation levels, using techniques such as connecting, building, embedding, and merging.
Regarding, the weight given to different phases of mixed methods, It is totally dependent upon the nature of question. For instance, if you need to explore first and then build a survey, instrument, or identify variables, use sequential exploratory. In this design, qualitative phase is given more weightage. On the other hand, if we want to see if both qualitative and quantitative findings complement each other, use convergent design. I would suggest for the details you refer to these methodological texts. In addition, explore the journals: Journal of Mixed Methods Research, International Journal of Multiple Research Approaches, and American Behavioral Scientist.
Creswell, J. W., & Plano Clark, V. L. (2018). Designing and conducting mixed methods research (3rd ed.). Los Angeles, CA: Sage.
Tashakkori, A., & Teddlie, C (2010), Handbook of mixed methods in social & behavioral research. Thousand Oaks, CA: Sage
Bazeley, P. (2018). Integrating analyses in mixed methods research. Los Angeles, CA: Sage.