I'm an older PhD applicant (Business-Marketing) with 20+ years of industry experience. In my SOP, should I include the several research projects I have already started, or should I focus on just one idea? Or should I reach out to a faculty member who might be interested in discussing my ideas first? I have no geographical ties, so I can go anywhere.
First, stop identifying yourself as an "older" PhD applicant. Instead, use some terms that come with more leverage like "mid-career." It implied that you're from an earlier cohort, and you also come with real world industrial experience.
Then, this statement:
I have no geographical ties, so I can go anywhere.
does not help because while it may appear flexible it also sounds clueless. Since you come from the industry, do you really think your industry welcomes any one with a PhD from any country? I'd suggest try talk to your peers and get a sense of where they studied or what degrees and institutions seem to be well-respected by them. You can also browse some related academic or business journals for some ideas on hot topics and prominent institutes.
As for how PhD application works... it's as varying as everyone's favorite grandma's recipe. Some will give you scholarship based on merit, some will require a professor's endorsement to pay for you, some will only consider if you come with a research grant/fellowship... that's why devising application strategies now without a shortlist of schools is just going to waste a lot of time.
Compared to the number of research interests, it's more important to think about if they are relevant to the faculty, well-balanced between realistic and ambitious, insightful in the short- and long-term plans, and genuine/authentic. The magic number will rely on your stated reasons for doing a PhD at that particular institute. A very general recommendation I often give is to diversify into a main thematic interest, a sub-thematic interest, and a methodological interest. I like this layout because it shows the applicant is not a one-trick pony, and yet not spreading overly thin nor easily distracted, and the last methodological interest can emphasize the applicant's flexibility, strengthening the potential as a collaborator.
In any case, do the research. Decide on some schools from different tiers, and start knowing them. Website, brochures, information sessions, booths at business conferences, etc. are all very accessible resources.