Counties - yes. They start at the top of the page, with County spelled out, and ditto down from there.
Doctor Franklin was four years old. I don't see any indication that his age was stated in months. For an infant, it would usually say 4/12 (see Sena (?) Wilcox, Line 22). I can't explain his name, but subsequent censuses and other records might clarify both name and age.
Mr Britt was a cooper by trade.
There was a Doctor Franklin Houston who served in the 27th Mississippi Infantry, and was captured at Kenasaw Mountain, Georgia, and joined the US Army in 1865. He would have joined the Confederate Army at about 16, which is young but not impossible.
"United States Civil War Soldiers Index, 1861-1865," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FSQC-LM4 : 4 December 2014), Doctor Franklin Houston, , Company , 5th Regiment, US Volunteer Infantry, Union; citing NARA microfilm publication M1290 (Washington D.C.: National Archives and Records Administration, n.d.), roll 24; FHL microfilm 1,604,907.