What happens to the Republic after Ruusan? Any wars?
No fullscale wars, no. The Republic becomes complacent and slovenly in the centuries after the New Sith Wars, which leads to the growth of crime syndicates and localized conflicts between individual planets/systems. This is what ultimately causes the Clone Wars.
Yes. My own timeline marked the rise of the Hutts and the Megacorps (Kuat Drive Yards etc.) in the 200 years preceding the Clone Wars. The Clone Masters were the most powerful of these. But for about 700 years before this the Republic experienced it’s Golden Age.