How to implement a software development process in an existing project?

My question involves setting up a Software Development process. If you came in to an existing project that had no formal methodology or process set up, and then were asked to set one up yourself, how would you handle it? I have looked into various methodologies like Agile, or subsets thereof like XP, but these are primarily aimed at how to set up new projects. I am rather unsure how to implement them into an existing project.

Best method to implement a filtered search

I would like to ask you, your opinion when it comes to implement a filtered search form. Let’s imagine the following case:

What methodology to use for planning/developing a Language conversion project?

I am trying to help my friend by creating a part of his on-going project.

Are Scrum and XP comparable things or are they used for different things

Are Scrum and XP comparable things or are they used for different things? what is the main features of each of them? how do they overlap?

How to sell logistical procedures that require less time to perform but more finesse?

I am working with a group where part of the responsibilities is managing a certain set of configuration files which, of course, have the same skeleton/structure across different environments but different values (like server, user, this setting, that setting etc.). Pretty classic scenario…

Scrum got specific ways for testing software?

When reading Scrum Guide, as the official text for scrum, I find out there is no specific solution to provide software testing in scrum. (the only hint is on page15)

For small-ish programs, should a single method handle most method calls to centralize program flow?

I’m fairly new to OOP (and programming in general), but what I find myself doing is that in the event that I don’t need to pass a value from one method to another, I’ll have my method calls centralized in some class within a Form.cs file.

How to avoid duplication between my issue tracker and the project specification documents?

I used to work for a professional consulting firm, and we worked under many different contract terms. When we could get a time & materials project, we ran it with SCRUM and tracked the backlog in our issue tracker system.

Is the following diagrams correct for RAD and Agile methodologies?

I do not know if this would be the right stack exchange site to ask this question but I have been researching on RAD (Rapid Application Development) and Agile methodologies and was trying to find their diagrams but if I google images this, it comes up with many different diagrams. So based on the images I drew my own diagrams on this.

Asking for suggestion/idea

currently we generate a quarterly PowerPoint report that includes tables and charts. The generation process of this report is quite cumbersome. First, numbers are generated in SPSS and then pasted into Excel. In Excel, charts and formatted tables are created and then exported onto PowerPoint slides. I am considering transferring this task to R in order to avoid the copy and paste method and generate all slides from there. This approach would also require less work in the future as only numbers would need to be updated. However, I would like to hear some suggestions about R presentation packages, such as R-Markdown, and any general suggestions based on your experience.
Thank you.