Theres a lot here, so I'll take what I can answer and address them individually...

What about the rank and file? This is a great question. Sectional tension among officers gets a lot of attention. It's pretty common knowledge southern officers defected from the military in droves, especially after President Lincoln issued an order that required officers to swear a new oath of loyalty to the United States. There were 1,108 officers in the U.S. Army in December 1860, and of these 270 joined the rebellion. That said, enlisted men to remained solidly loyal to the United States.

The most important reason for this is that enlisted soldiers in the prewar regular Army tended to either be foreign-born immigrants or urban northerners who were (unsurprisingly) loyal to the Union and had no reason to support a slaveholder's revolt. For example, when the 10th U.S. Infantry was organized in 1855, of the first 500 men who joined the regiment, 66 were from New England, 149 were from the west and midwest, and 285 were foreign-born—none were from the south.

Military colleges in the South Yes, there were a ton of military colleges in the south, but you have to remember that most graduates of these schools did not join the Army as officers. Most graduates joined local and state militias, and receiving a military education at one of these schools was more of a class and cultural act than a desire to join the U.S. Army. It was also a symbol of white racial solidarity, since much of the south's martial culture was based on fighting Indians and preventing/suppressing slave revolts. But, if you were a nineteenth-century white southerner intent on a career in the regular Army, you're goal was to get into West Point. That said, loads of southerners went to West Point and were commissioned as Army officers. But they were still in the minority.

Soldiers following generals to the Confederacy Like I said previously, most rank-and-file soldiers remained loyal to the United States. If any soldiers followed their commanding general into rebellion, there weren't many. Pre-Civil War officers tended to rule their commands with an iron fist—discipline was notoriously bad in the Army, and many soldiers felt free to desert the ranks if they weren't happy. In the 10th Infantry (the regiment I mentioned earlier), 55% of the first 500 enlistees deserted before their first contract ended. If you were a lifer, you tended to serve in the same regiment for your entire career, so your loyalty would have been with the regiment, not the commander (who changed pretty regularly). If you weren't a lifer, you probably weren't loyal to a general, and you certainly wouldn't have followed one to the Confederacy.

*Did they resign and head south? I can't really speak to enlisted men, but my educated guess is yes. Like I said, desertions were common even before the Civil War, and most deserters were never caught (some even successfully joined the Army two or three times under multiple names). We also know that the vast majority of southern officers resigned their commissions with without any resistance from the Army.