Is the Valley Forge in the film 'Silent Running' the same one as in 'Battlestar Galactica'?

Yes. However, what was used for Galactica was actually stock footage from Silent Running. Seeing as both the film and Galactica are Universal properties, use of the footage wasn't a problem. It was most likely John Dykstra who purloined the footage, as he did the SFX for Galactica and also worked on Silent Running. The Valley Forge model was disassembled after the filming of Silent Running, and is said to have been destroyed. However, a surviving forest Dome from the model was purchased for $11,000 at auction in 2003, and now exists in the Science Fiction Hall of Fame Museum in Seattle, WA.