1) Grant was acting on Halleck's orders, so these motivations that have been ascribed to Grant that should appropriately be ascribed to Halleck.
2) As far as I know, we're left to speculate on Halleck's motivations. Halleck either distrusted McClernand's military competency, his political grandstanding, or both. Although I believe Parker Hills and Terry Winschel disagree, I think Halleck was absolutely correct in this regard, McClernand was a brave but incompetent commander. McClernand's Corps was involved in three Vicksburg Campaign battles prior to the seige: Port Gibson, Champion Hill, and Big Black River. Port Gibson and Champion Hill are both damning performances, and McClernand was not even in command at Big Black River (Grant had placed Eugene Carr in command of the pursuing force after Champion Hill).
3) McClernand did not raise the troops that were at Memphis, I believe the most you could say in this regard is that he expedited the process of forwarding the troops to Memphis.