If Confederate forces collapse at Bull Run it won't END the war, however it will drastically alter it. Richmond will likely fall as the defenses there were rudimentary (and that is being generous), assuming McDowell can keep control of his troops. something that is far from a given. Even if Richmond does not fall, the message regarding its apparent hideous vulnerably will not be lost. It is likely that you see the Capital moved Southwest, possibly to Atlanta or Montgomery.
The biggest difference, of course, is the shattering of Confederate confidence and the likely destruction of the myth that grew around the innate strength of "Johnny Reb" as a solider. In a rout there is also a better than even chance that Jackson and his command wind up being overrun and obliterated, robbing the Confederacy of that man's mad genius on the battlefield.
However, to go to your second point, namely slavery, there chances of it actually simply disappearing are nil. What really destroyed slavery was the fact that the War continued long enough that Lincoln decided to play a card in hopes of bringing several border states, especially Virginia, back to the Union. The Emancipation Proclamation, as much as it is justly celebrated, was designed as a "carrot & stick" tactic. It only applied to areas that were still in rebellion after its effective date, meaning any state that returned to fold would return with slavery, and the almost mind numbing wealth slaves represented (the value of all the slave in the South at the start of the ACW exceeded the entire Federal Budget for several YEARS), preserved. Only when the Confederacy held firm did slavery effectively die (of course it took the 13th Amendment to formalize the end of the despicable Institution).
Without the Proclamation the only way to end Slavery would have been via an Amendment. That would require a 2/3 vote in both chambers, which would be extremely unlikely (the 13th Amendment failed the first vote in Congress DURING THE WAR, even some War Democrats though it went too far) add in the Southern States and the proposed Amendment is probably outright defeated. Then, it will require 3/4 of the states to ratify the Amendment. In 1861 there were only 34 states (West Virginia wasn't admitted until 1863 and then only because Virginia was in secession) meaning 26 states need to ratify. There were 11 Slave States. It wasn't until 1896, with the admission of Utah, that there were enough states to Rarify (assuming ALL new states were "Free Soil" and voted to Ratify, and none of the Slave states crosses the Aisle, none of which is an absolute given).
