The plan, as detailed by Rosecrans, was to cut off the ability of the Army of the West to move out of Iuka, either to the south, to the east via Bear Creek, or to the north (or obviously to the west, which wasn't considered a serious threat, for obvious reasons). We do know that.
No, it was not necessary to move a mile eastwards out of Iuka to reach the Fulton road.
As can be seen above, another reversal on the bridge claim has come about just several hours after the last one.
No, the correspondence pertaining to crushing in the Confederate left dealt specifically with the ability of the Army of the West to pull out of Iuka eastwards, as is obvious to anyone reading the relevant correspondence. That assertion can't be reconciled with the available record and hence must essentially be dismissed.