What are those plugs called, and who is the manufacturer?

They are mini-banana plugs and jacks. Pomona is one company that makes them:

http://www.pomonaelectronics.com/pdf/d2945_100.pdf

http://www.pomonaelectronics.com/pdf/d2143_1_01.pdf

Digi-Key stocks them.

Those look very much like the connectors that Märklin uses for their model trains, the good old analog version.