Yes, it's one of Camp Kirkland's practices to put a short strain of one song instrumentally in between the choral ones. In a similar manner, you may have noticed a few notes of "America The Beautiful" around 2:40, in between the Air Force and Marines songs. They're the notes where "O beautiful for spacious skies..." would be sung, perhaps referring to the Air Force keeping the skies free. Then again, I may be trying to read more into it than I should!
With respect to all the clapping, while I was not AT this concert what usually happens is that each service members' veterans will be encouraged to stand in the audience as their song is heard. The audience is acknowledging those that are standing that are outside the view of the camera, so it SOUNDS excessive, but the intention is to honor those that have served... not to be overly zealous with the clapping! :-) Hope that helps with understanding why all the clapping is heard.
