Death from disease Union- 249,458 Confederacy-164,000 total 413,458
source http://www.learnnc.org/lp/editions/nchist-civilwar/4601
Was there a mad rush to remedy?
Dysentery. This one disease accounted for around 45,000 deaths in the Union army and around 50,000 deaths in the Confederate army.
Typhoid was another major killer. Again this disease was a result of contaminated water or food. Typhoid killed around 30,000 Confederate and 35,000 Union troops during the war. 1 out of every 3 people who contracted this disease died of it.
Thanks in large part to Florence Nightingale, pioneer of professional nursing and info-graphics, we have detailed accounts of the casualty rates for a European theatre of war roughly contemporaneous with the American Civil war.
The Crimean war was fought between October 1853 – February 1856 and the casualties for the British and French Empires were listed as follows
British:
Total dead: 21,097 of which : 2,755 killed in action;
2,019 died of wounds;
16,000 - 16,323 died of disease
French
Total dead: 95,000 of which:
10,240 killed in action;
20,000 died of wounds;
approx 60,000 died of disease
As you can see from these figures, disease and wound infection claimed far, far more victims than the military engagements themselves.
http://en.wikipedia.org/wiki/Crimean_War
http://plus.maths.org/content/florence-nightingale-compassionate-statistician
There's a chapter on this in McPherson's Battle Cry of Freedom. Here's a relevant passage that goes a long way toward answering your first question:
Disease was a greater threat to the health of Civil War soldiers than enemy weapons. This had been true of every army in history. Civil War armies actually suffered comparatively less disease mortality than any previous army. While two Union or Confederate soldiers died of disease for each one killed in combat, the ratio for British soldiers in the Napoleonic and Crimean wars had been eight to one and four to one. For the American army in the Mexican War it had been seven to one. Only by twentieth-century standards was Civil War disease mortality high.
Ch. 15, sec. IV.