Yes and no, depending on your definition. Yes, you can do valid qualitative research without collecting data in the field. For example, all literary research and much historical and legal research is based on analysis of documents. That is, if you define “data collection tools or techniques” as collecting new data in the field then, Yes, you can do a qualitative study without any data collection tools or techniques. (By the way some kinds of quantitative research use existing sets of statistical data.)
However, you cannot do research of any kind that I know without some kind of data. It’s like trying to eat without food. That is, if you define “data collection tools or techniques” as collecting data of any kind then, No, you cannot do a qualitative study without any data collection tools or techniques.
It depends on the style of argumentation. When the method is primarily analysis and critique of existing documents about theory, you normally don't need a methodology chapter, although the introduction should include assumptions and delimitations.
Another kind of research might not need much in methodology. In some ethnographic works, the section on methodology might be so brief that it is placed in the introduction. However, demographics and context might be so major that they require their own chapter.
The issue is alignment. The research problem, the methodology, and the kind of data have to align. Several outcomes of an incorrect methodology are likely:
In some cases it is quite feasible to have data of all members of the research population, such as existing datasets.
In other cases, researchers carefully qualify their conclusions or must choose a different population.Otherwise, it depends on the kind of study:
It is a small group from a much larger group, but your conclusions from the sample allows you to draw conclusions that apply to the whole group. There many different kinds of sampling techniques, and the selection of the technique depends on the kind of research and purpose.
It depends on the institution, the field, and the topic. For example a dissertation might need a whole chapter on social and cultural context, or on the epistemology of the topic.
Some institutions use the “standard” series of chapters for all dissertations (1. Introduction 2. Literature review 3. Methodology 4. Analysis 5. Conclusion) and it's a good idea when the school requires a fairly uniform procedure for progressing students.
In principle, yes, and some dissertations do so. I should qualify that by saying that it depends on the topic. If your advisor says it is not enough, he/she probably has specific reasons and you need to know what they are.
The literature review is a picture of the current state of research relevant to the research question, and usually involves critique. However “critique" is not just fault-finding and may also include pointing out strengths of important works of research and drawing together common themes from disparate bodies of literature.
The methodology chapter describes the method the researcher will use to gather data that will resolve the research question. In one way, it is the next step; how to get from "what is currently known" to “how to get to what we need to know.”
First, how good is the research problem? I hate to be cynical, but this kind of question is most common when the topic is ridiculous. For example “How could I learn X about the fairies at the bottom of the garden?” Upon criticism of the topic, these people respond, “But you’re just a fairy hater.”
Okay, let's progress on the basis that your research question is a good one.
It is almost certain that standards apply, but perhaps not very directly. Whatever methodology you come up with, you will have to demonstrate its validity somehow.
This sounds like a case where one would need to be innovative in methodology. In some cases, an innovative methodology is a paper in itself, and can also mean the difference between a rather mundane piece of research and something much more valuable.