As a general answer to most of your questions, and also this is not the only answer to why so many did enlist. But, be aware that not all these desertion/enlistments were as voluntary as they may appear.

It was a common practise of both side especially in the later years, Since, the Union and the Confederacy, both had conscription law, to send their cavalry on patrol and if they came across a man of military age, they ask him if he was loyal to the "cause"(North or South)? If the man replied "NO", then he was in trouble. If he answered "YES", then they asked him why wasn't he in the service? Which left the man little choice but to enlist.

This practise was particularly used by the Union Cavalry to root out confederate sympithizers when they moved into an area.

The Confederates usually didn't know what had happen to their men who had gone home to recover from Illness, wounds, on furlough, or to harvest the corn crop, etc. etc., Naturally, they recorded the failure to return to duty as "deserted". The Combined Service Records compiled much later after the war simply put the two events "Deserted CS/Enlisted US" together as a continuing single record.

This doesn't explain all those enlistments. There were indeed changes of attutide as the war progressed but there was a multitude of circumstances which caused these "changes" of attitude. The same of the Oath of Allegience.