Ashley,
Below is a link for a capsule history of the Fourth Tennessee Cavalry Regiment(US).
http://www.tngenweb.org/civilwar/usacav/usa4cav.html
As far as pictures, it is possible you may find a handful of pictures of individuals that may have served in that regiment, however, it is rare and doubtful you will find a "group" or formation photo. I recommend you research regimental history, re-enacting, or ancestry websites to see what you can glean.
I am not sure of the second sentence. What question are you asking? What application? There is no such thing as an "application for war". Are you asking about an Federal Indigent Veteran's or Widow's pension application? Are you asking about a copy of the Compiled Military Service Record?
Thanks.
Respectfully,
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment
http://39thgavolinfrgt.homestead.com/39thHomepage.html