I think you are forgetting a few facts here. For one, Robb still has Jaime as a hostage and that could prolong the conflict considering that the Lannister's have none. Would Robb contemplate trading Arya when nobody has seen her anywhere near the Lannister's and they refuse to provide proof they even had her? Would Tywin even contemplate a red wedding like scenario when Jaime could get killed?
Jaime will likely escape from Robb's camp if another prisoner is put into the same cage as him, as per canon. With Joffrey dead, Jaime might be motivated to break out of jail faster, fearing that something bad could befall his other two children.
If Jaime is still captive by the time the red wedding would have happened, I can see Twyin going ahead with it anyway. He loves Jaime but he's not going to pass up the opportunity to end the war right there. Also, with the help of the Freys and the Boltons, there is a decent chance Jaime will survive the ordeal.
the death of his sister in such a public/horrific way will definitely affect the way he acts. He might accelerate his campaign or who knows what else, and if that affects or throws off Robb consorting with Jeyne Westerling the war definitely will drag on longer as Roose won't try anything without the Freys helping.
I think Catelyn would grieve the death of Sansa but would fear for the rest of her children and try to reign in Robb and prevent him from being too reckless. Unfortunately, canon Robb was already reckless so I could see him diving headlong into the lion's jaws.
Also, even if the Freys and the Boltons don't ambush Robb at the Twins, there are plenty of other points at which they can ambush Robb. If Robb leads an expedition into the Crownlands or the Westerlands, he will be very far from home. It would be pretty easy for the Bolton and Frey armies to help the Lannisters encircle Robb. Then again, logistics don't quite make much sense in the setting, as
@Aldarion has pointed out before. If we go with the idea that Westeros is actually continent sized, then the logistics train is just impossible to maintain for that far of a distance. If Westeros is actually Great Britain sized, than maybe. Ultimately Robb needs a lot of local help... but again, it's rather fragile for him.
What if Stannis decides to bypass going for Renly and a Mellisandre goes after Tommen? With his death Stannis would be the legitimate king, because their would be no male heirs in the line of succession.
Hm... perhaps. However, Twyin won't back down even if Tommen is assassinated. The death of two kings in a row would shake the loyalty of those pledged to the Lannisters, but the Lannisters would still be quite a problem. Even by themselves, they hold quite a defensible position.
If after Tommen died, the Tyrells joined Stannis, then I suppose Twyin would be in real trouble. Would be quite a brutal war trying to take King's Landing and Casterly Rock. If Stannis beats the Lannisters, then a peace could come over Westeros. He won't control the whole land but I don't see everybody fighting each other. Everyone might ally to repel Dany and the Others/Walkers.