Help regarding directory requirements

Hello,
We are a nonprofit and are new to WordPress and trying to figure out how best to create what we need and Name Directory sounds promising.

All we need is a simple site with one directory type of page. It should look exactly like this https://changingthepresent.org/collections/george-washington-high-school-10002

Note there are 140k schools, each of which will have a page like that.
We do not need a way to search for them, as that will happen on a separate site. But we need each school page to have its own URL so schools can link directly to their page.

Each of the “products” will be a student or a donation opportunity. Those pages will not be on the WP site. ALL the links on the school pages will go to a separate site. Student “products” have two links (profile and wish list, each on a separate site). We may have as many as 2k “products” in some schools, and a total of 5M – 10M products. Of course, we need pagination and caching.

We do need the filtering by tag as you see on the left WITHIN a school (not site-wide).
Search within a school would be nice but not essential, so long as we can filter on the left and show alphabetized results.
The two forms at the bottom are just iframe embeds.

Hence,
Can we do this with Name Directory?
Add Custom Post Types to accommodate the specific fields we need?
Use a specific theme? Again, we want it to look exactly like the page at that URL I cited.
MySQL database?
Do you provide tools to manage the connection to it?
We want to be able to add new products on the fly as we add them. Can we do that with Google Sheets, Zapier, Integromat, or something?
Do you recommend a specific hosting company for this? 5 to 10M records and 500k to
2M visits per month.

Any help or suggestions will be highly appreciated!!
Thanks.