Shiloh was another example of Grant's "learning curve." He always claimed he was not taken by surprise, but the evidence indicates otherwise. In particular, Grant refused or did not fully comprehend the importance of entrenching (at that stage of the war, maybe no one else did), and was beset by confused orders to Wallace and his Division. Grant can be credited with rallying the troops, but the battle was actually won by the arrival of Buell's army in the nick of time. Still, Grant was following on the heels of his victory at Fts. Henry and Donelson, so he must have retained much goodwill on the part of Lincoln.
100%. You might be onto something about Grant and his low-budget modesty. He failed at Iuka, and several times in front of Vicksburg, but Lincoln still kept him in command. As Lincoln said, "I can't spare this man, he fights." It was true, and apparently Lincoln saw something in him that forced him to keep him in command, even though other fighters, like Rosecrans and Hooker, were removed when they experienced setbacks. Perhaps there was something in Grant's dispatches or reports, which Lincoln may very well have read, that indicated a clear-headed, forthright, and aggressive commander.