That building is the Odyssey Restaurant. I don't know the specifics of when
it was in operation, but it has not been in regular operation in a long
time. In the early years I understand it did have character meals - probably the only
ones in EPCOT Center at the time. Nowadays it is mostly closed, opening only
for special occasions like the Food and Wine Festival, where they have
demonstrations, and business functions. I've also heard that Magical
Gatherings meet there. In the back, unseen by guests, is a Cast Member only
break area and food service.
You can access bathrooms on the left side and a first aid center and more bathrooms on the right side. I have to say, the bathrooms on the left are probably the nicest bathrooms inside a park at Disney.
Body Wars was in fact directed by Leonard Nimoy, and included actors Tim Matheson and Elizabeth Shue.
Originally planned to open with EPCOT Center, they were unable to sign a
sponsor until MetLife did several years later, and it opened in 1989.
MetLife eventually ended its sponsorship, and officially in 2004 Wonders of
Life was placed in the dreaded "seasonal" category, which means it is only
open in rare circumstances1. It was most recently opened for a few weeks in
December 2006 with limited attractions in operation.
The pavilion sign and the double helix were removed in August 2007, and it was announced that the pavilion would be used for part of the Food and Wine Festival in the Fall of 2007. How extensive any sort of renovations will be is unknown, but word is that Cranium Command and Body Wars are to be preserved somehow.
It all goes back to Walt Disney. His plan was not to build "Walt Disney World", his plan was to build "EPCOT", which as most know stands for the Experimental Prototype Community Of Tomorrow (sometimes City is substituted for Community). The Magic Kingdom was a part of the plan in the north of the property, with EPCOT Center in the center, and an airport to the south, connected by monorail. EPCOT Center would be an actual planned city, where Disney employees would live (rent only, no ownership), and hotels and other attractions. Visitors would pass through EPCOT Center on the way to the Magic Kingdom. The whole area would be called EPCOT.
There is a lot more to the story than I can say here, but in short with Walt's passing plans changed. EPCOT Center instead became a showcase of technology, and the property was more formally called "Walt Disney World". Even during the Wonderful World of Disney special on the opening of EPCOT Center, Danny Kaye attempted to explain that EPCOT and Walt Disney World were the same thing.