Yes, Lincoln attempted to start war at Fort Pickens. He issued verbal orders to General Scott on March 5 to reinforce Fort Pickens. The reinforcement didn't actually take place until April 11th.
Perhaps the following would lay out the sequence of events for you: [Link]
Also, the following extensive report by Gideon Welles mentions direct orders to Porter that he enter Pensacola Harbor. It makes reference in a couple of places of the ship "running the batteries", in one instance of running by the batteries of Fort Barrancas (across the bay from Fort Pickens). The Confederates held Barrancas at that point, but probably didn't have it extensively manned. I'm not sure whether Porter was ordered to run the ship by Barrancas flying English colors, fire at the fort, and be fired at, and possibly be sunk as a way of starting the war. That is speculation on my part. I haven't seen Porter's orders.
Here's the Link2.
By the time the Powhatan arrived, Fort Pickens had already been reinforced on the night of the 11th (before Fort Sumter was fired at). There is documentation for that reinforcement on the 11th.
There were two sets of conflicting orders from Lincoln concerning Pensacola Harbor. One to Colonel Brown placing him in overall charge of the Union forces there, and one order, whatever it was, telling Porter what to do. Brown prevailed.
No, in fact, Lincoln merely attempted to repeat resupply missions first sent by President Buchanan in January.
Neither Buchanan nor Lincoln wanted to "start war" at either Pickens or Sumter.
They did wish to hold those forts, indefinitely.
So the decision to use Union resupply/reinforcement missions as excuse to start war was strictly Jefferson Davis'.