As lentulusgracchus has pointed out, war was the responsibility of Congress. Lincoln was clearly on the path that would result in war.
The Senate usually had special sessions every two years at the end of the regular session, sometimes longer, sometimes shorter. So, this special session was by no means unique. Doubtless, the new president had appointments he wanted to make, and some of the higher ranking ones required Senate confirmation. The new government needed to be set up.
In checking the minutes of this special session I see where Lincoln's secretary Nicolay would periodically bring in communications from the president, and the Senate would then go into executive session to discuss them.
The session had opened with Lincoln's inaugural address. There then followed quite a bit of discussion on what Lincoln meant in the inaugural and whether the Senate should print the inaugural speech, which was apparently not usually done. A number of other things were discussed including whether to expel Senator Wigfall of Texas since his state had seceded, but he was staying in the Senate until he was officially informed of the secession. There was discussion about forts in the seceded states and what the administration intended to do about Fort Sumter. One argument at that time was that Sumter should be evacuated as a military necessity. There were not enough troops to force their way in to the fort, which was apparently true if Scott's and Anderson's manpower estimates were correct.
Bottom line on all this: Lincoln came out and said that he wasn't going to start shooting first.
Could the South trust anything that Lincoln said? He sent Lamon to Charleston to say that Sumter would be evacuated. It wasn't. His Secretary of State similarly assured the Confederate Commissioners about Sumter, and they ended up accusing the Administration of gross perfidy concerning Sumter. Lincoln sent Fox down to visit Sumter, and Fox was allowed to visit Sumter for supposedly a peaceful purpose but in reality Fox was planning his Sumter relief expedition as became clear by some captured communication, IIRC. Lincoln said the Union couldn't stand half free, half slave, yet he supported a constitutional amendment leaving slavery alone in those states that wanted it. Which Lincoln was president?
What was to prevent a not-so-trustworthy Lincoln from reinforcing Sumter with men and ammunition instead of just supplying the fort with food? Until news began leaking out that an armada of war ships was being prepared by the North the Confederates had allowed Anderson to buy food in town for the fort. Anderson had earlier turned down an offer from the governor for free food; he insisted on paying for it.
The Richmond Daily Dispatch of April 5, 1861 said the following (I have no idea whether it was true -- it doesn't seem to match the story that the North/Anderson was putting out):
The Mercury has a correspondent who says:
Up to this time, two hundred pounds fresh beef, and three dozen cabbages, have been sent to Fort Sumter three times a week — besides potatoes by the barrel. Thus, both officers and privates have been allowed to have at least a considerable amount of wholesome provisions fer seventy men, and what cause is there for complaint? These facts are derived from the best authority, and are reliable. Let the Northern people do justice to Southern liberality.
As a Monday morning quarterback I would not have stopped food supplies and instead have widely publicized that the South was providing all the food that the fort needed, leaving no justification for Lincoln's supply-Sumter-with-bread Expedition.
If Davis or Pickens had bothered to read or understand Lincoln's inaugural, they might have let Lincoln start the war that you guys are so certain that he wanted, and let him bear the consequences.
I've seen it argued that there was a chance that one or more already-seceded Southern states might waiver about their secession if Davis et al. let Lincoln supply the fort. I don't know whether that was true or not. I doubt it. More probably Davis recognized that a confrontation with the North would drive more states into the Confederacy, just as Lincoln recognized that such a confrontation would firm up support for himself. Both things happened.
By itself SC was too small to be a country, too large to be an asylum. They needed Virginia. They started the war to bring in Virginia. Virginia showed the bad judgement to let themselves be suckered in.
Maybe, maybe not. But if you expect a declaration of war every time the US fights, you must have been disappointed over the last 70 years or so. In this case, though, you weren't going to get a formal declaration of war, because that would have meant recognition of the Confederacy as an independent state.
What you ought to do is find a neutral baseline. When domestic strife threatened -- the Whiskey Rebellion, the nullification crisis, Indian Wars, prolonged strikes, race riots, draft riots, civic unrest -- was Congress called in to session to deal with such problems or wasn't it? I suspect the answer is that it was assumed that the administrative authorities would have to deal with immediate crises, and Congress was only summoned later to change the general policies by enacting new laws.
Also, get in touch with your inner Dick Cheney. Surely, the executive does have some legitimate responsibilities and prerogatives that Congress can infringe upon and erode. Believing that doesn't make one a tyrant or supporter of tyranny, does it? Nobody expected any kind of declaration of war, and if the Senate thought it could handle the situation, it wouldn't have adjourned.
Could the South trust anything that Lincoln said?
What was he going to do? Call in an air strike? Put a nuke in with the food and medicine?
I guess you could "trust" secessionist mobs and militia to seize whatever federal property that they could within their borders and Confederate secession commissioners to foment rebellion further away, but such behavior was hardly conducive to peace and reconciliation.
Early on, the advantages on the ground were with the rebels. They had the advantages in local conflicts. They could simply seize (or demand and then seize) federal positions and property. There was some uncertainty given that state and confederate officials might not be on the same page, but I guess you could "trust" them to grab whatever they could.
Things were different with the federal government. Buchanan and Lincoln weren't of the same opinion. What Buchanan gave away Lincoln might not want to surrender. Within each administration, different officials spoke with different voices. Some of Buchanan's appointees actively supported the secessionists. And local commanders on the ground, hundreds of miles from Washington, were apt to act on their own initiative.
Lincoln wanted to maintain some symbol of federal authority in the rebel zone, but what would that be? Which fort? Moultrie, Sumter, Pickens, Jefferson, Taylor? Each had disadvantages that it may have been hard to see clearly from Washington DC. And conditions changed over time in ways that might not be foreseen.
When secessionists could simply grab whatever they wanted, unionists had to delay and rely on strategy. That shouldn't be so surprising. During the war, when the Federals had the advantage of greater strength, the Confederates had to rely on their wits and guile.
So, trust is a two-way street. Trust has to be earned. Trust is not absolute in situations where two parties are competing or struggling with each other. Trust is going to be a partial or relative thing.
Still, there were limits on what Lincoln would do. If he actually did try to trick his opponents, he would lose support both in the Upper South and in the North. If he sent troops and ammunition to Sumter instead of bread and medicine, he would be exposed as deceitful. And what would it gain him? A few weeks more time? Was it worth it? If he sent a war fleet into Charleston Harbor after declaring that he only wanted to feed the troops at Sumter wouldn't that likewise weaken his popularity and authority?
So I don't buy the argument that some suspected Lincoln ruse justified beginning the war. This was a situation in which much maneuver and jockeying and a certain amount of cleverness was required. It was also one in which outright, planned deceit wouldn't be rewarded. To say that not trusting Lincoln justified the attack, is to say that because you didn't get what you wanted when you wanted it you were justified in firing the first shot.
Lincoln spelled it out in his inaugural: he wouldn't attack, and if Davis wanted a war, he would have to start it himself. Lincoln put his reputation on the line, and made it clear to Davis that any war was Davis's to start or not. That doesn't look like much of a trick.
Lincoln said the Union couldn't stand half free, half slave, yet he supported a constitutional amendment leaving slavery alone in those states that wanted it. Which Lincoln was president?
If you've never had to do something tactically that you might not have approved of in your larger theoretical scheme of things, then you've never been in politics. In any case, Davis and Lee pledged themselves even more solemnly to things that they abandoned when circumstances changed. I guess they also weren't to be trusted either.