Remain vs. Remains

It should be "remain" since it refers to "partnerships". If you rewrote it as:

"Founded in 1900, Company XYZ remains one of the few true partnerships among the top banking firms of the world. "

Then use "remains" because it refers to the singular "Company XYZ"

one remains

Yes, "one" remains

It is not stated how many true partnerships remain; what is stated is that few (and that means a small number, more than one) do, and that Company XYZ is one of them.

One of the few that remain. Few is not one.

It should be 'remain'. Few true partnerships remain. Company XYZ is one of them. My father is one of the few people still alive who fought right through World War 2. My car is one of the few 1973 VW Beetles that remain. My sister is one of the many people who like chocolate.

Yes, partnerships remain. It's a plural.