It is important to remember that the Democrats of the Deep South weren’t really looking to avoid war. Every day in every way, the North was getting more populous and economically powerful. The longer the Southerners waited, the weaker they would become. That was why it was so important for the Southern Fire-eaters like Rhett and Davis to provoke a crisis. Better in 1860 then ten years from now, when they would be weaker.
The move to split the Democratic Party in 1860 was a deliberate attempt to destroy the Union and elect a Republican to the Presidency. They could use that as an excuse to secede from the Union.
No he would not. Lincoln took 180 electoral votes, almost 60% of the total. In all but two states, California and Oregon, he took an absolute majority of the votes cast. So even if Douglas and Breckenridge had not split the Democrat vote Lincoln still would have won the state and at least 173 electoral votes. More than enough to win.