Clarification on Software Development Jargon and Terms

Hi guys, I'm a typical business analyst that's trying to wrap my head around all of the software development jargon that's out there in industry. I get the feeling that not everyone is on the same page, especially on the business side of the house, as to what agile, devops, and SDLC is.

1. To start off, after reading up on the Agile Manifesto and the various agile methodologies out there, I feel like many of the methodologies out there are counter to the principles espoused by the manifesto. In fact, the whole concept of an "agile methodology" seems counter to the Agile Manifesto; Individuals and Interactions over Processes and Tools. Many of the current discussions at my organization surrounds selecting the best PPM tools for managing agile projects and designing processes and controls the monitor the health and status of Agile development. Additionally, many of the methodologies seem to be shortening waterfall projects into "Product Increments" and changing software development into a never ending series of "increments". Does anyone else feel like this? What's worked within your organization in terms of adopting agile for software development?
2. I've never led the development of software before, but as I understand it, there are 7 main phases of an SDLC. (1) Planning, (2) Defining, (3) Designing, (4) Development, (5) Testing, (6) Deployment, and (7) Maintenance. The most popular project management techniques are Agile and Waterfall. In Agile development, does the project start with product increments that are specifically focused on planning, defining, and designing? Increments that doesn't touch the software at all? I'm running an issue in a systems modernization where the business leaders seem confused about the vision of what the new modernized system should look like. For example, I can describe to our developers the current processes and features of our legacy system, but we don't have the buy-in from executives to develop new features as it would require participation from other business units. In this case, should we as an organization, have pitched the modernization efforts internally and made sure we had buy-in, before we started the development? Right now we're undergoing a modernization effort that doesn't seem to be delivering new features or capabilities outside of what our legacy system already does. It seems like some executives sees Agile as a silver bullet for all "change" but did not have the foresight to do any planning, defining, or designing prior to contracting development work to a third party vendor. I feel like this project has a high probability for failure and will require a lot of rework down the line.
3. Our enterprise IT portfolio is currently made up of "IT Investments"; don't worry about the term investments, it's literally just a bucket of money that a specific business unit has for any fiscal year. There's a want to switch from our current portfolio structure from the nebulous investments to "Products" and "Services". I know the term "Product" is a common term in software development, but does anyone know of software development teams that develop "services"? In some sense, "Products" could be synonymous to "Services". Does anyone know how a PPM structure that rolls up development projects up into "Services"?

Thanks for the feedback!