If our solar system some how captured a rogue planet, and it orbited the sun in the opposite direction to all the other planets,
what major affect would it have on the stability, would its drag cause all the other planets to slow down ?
could it be possible for it to be sustained at all ?
Totally dependent on the details. A rogue planet could be any mass from Pluto to 10 Jupiter masses - quite different gravitationally.
And exactly what it's trajectory was makes a huge difference. If it came barreling into the inner system it could cause chaos, particularly a large body.
It would certainly have to pass thought the Oort cloud and possibly the Kuiper Belt. Any appreciable mass doing would disturb many, many objects which have the potential to fall into the inner solar system (or not). So that alone could be dangerous for us (or not). It's a dice throw - quite random from our point of view.
Stable is relative. If it disturbed orbits in such a way that in a hundred thousand years Earth would become uninhabitable that might be not too bad - a lot can happen to a species in that time scale, especially one armed with nukes. :-) So this isn't a question with a single answer.
Answering one question: gravitational drag is primarily a function of where the two bodies are. This means that any time one planet "lags" another the lead planet is slowed slightly by the gravitational pull. A planet in retrograde orbit would simply reverse the portions of relative orbital position where gravity slows or accelerates each planet's speed.
