It all depends on what you mean by faulty. If the rack has wear in it and isn’t as tight or responsive as it should be, then it will continue to wear out further (and eventually fail) but shouldn’t affect the car beyond that. If, however, you mean the rack is dangerously loose or about to break or come apart at some crucial point, you stand to destroy the car in a crash and perhaps injure yourself or someone else. Or worse.

Fundamentally, there’s no margin for error with a car’s steering. If it’s not right, the car should not be driven at all and should be fixed properly before it hits the road again. Provided you can find a second-hand steering rack with no wear and in perfect condition, then it should be fine to use. But again, don’t take chances with any of this. And make doubly sure there’s no damage to the rack and its fittings such as from a previous crash. Ask yourself why the original car donated this second-hand steering rack in the first place.

This could be a coincidence whereby your maintenance was timed perfectly with something else going wrong. But if we assume that the new fuel filter is what has caused the no-start condition, then the first thing to check is that you've installed the filter in the correct orientation. Many filters only operate in one direction. Install it backwards, and the fuel may not flow at all, which would give you the symptoms you're now looking at.

The Mazda3 and Holden Astra are both good alternative choices, but you could also consider a Toyota Corolla or Kia Rio or Cerato.