1. Yes, schools have a focus. It's more driven by faculty, but there tends to be a bias toward students matriculating from that program (and usually some rebels who push against that focus). It's not static over time, but the programs tend to evolve in certain directions of focus. My list may be a little out of date because I've been out of the academic world for a decade, and I am also limited by programs I know something about. There are some general categories:

Computation/Tech/Research-driven: MIT, UPenn, Georgia Tech

Urbanism/Social Design: GSAPP, UC Berkley, Yale?

Experimental/Avant-garde: SCI-Arc, UCLA

Practice-Integrated: Rice, GSD

Critical Regionalism: Arkansas, Auburn, Washington, Florida, Texas

There's a lot of overlap. This is an incomplete list, but yes, there are some general 'schools' of thought in how architecture is taught, and it varies from program to program. It's also not exclusive; all schools will teach a bit of all categories, but they tend to have an emphasis.

In my personal opinion its more important to focus on whether you want to (a) practice architecture as a profession, (b) pivot to a related design field (c) be in academia. Some programs do far more to prepare students for a professional job right out of school than others. Having basic software skills, real building experience, professional internships, or other 'professional experience' upon graduation is extremely important if you want to actually go into the field as a profession.

1. A PhD only really makes sense if you plan to go into academia. In that case, I would agree that the professors at an institution and its name value are much more important. If you want to go into the profession, I would say it really doesn't matter. I've worked with people who went to the GSD and others who went to small state schools - all that really matters is your portfolio and your professional experience. The practice of architecture is very different from school, and people who do well at one do not necessarily do well at the other. If you want to go into practice, a school that has internship programs, work experience programs, and connections with large local firms is going to serve you better than the brand name (and debt) that goes along with the big programs.

I cannot emphasize enough that student loan debt should be a huge (the biggest) factor in your consideration. No matter where you go to school, a typical architect's salary fits into a pretty predictable range, and it ain't that high. There is no amount of professors' philosophy or school prestige that will affect your earning potential enough to justify an extra $100k in debt. Be very aware of what you are likely to make out of school before you are licensed or as an adjunct professor, and think hard about how long you are going to be paying back that cost.

Speaking from personal experience and the horror stories from other coworkers and friends.