Learn Russian: Женщина не катит коляску на крутой склон. - The woman is not pushing the stroller up the steep slope.

Катит is the unidirectional verb for rolling or pushing a wheeled object. It is used here because the motion is happening in one specific direction (up the slope). If she were pushing the stroller back and forth or generally walking it around a park, you would use the multidirectional verb катает.

The English translation says pushing. Why do we use катить instead of the general verb for push, толкать?

While толкать means to push, Russian specifically uses rolling verbs like катить and катать for moving objects on wheels. Pushing a stroller, a wheelchair, a bicycle, or a shopping cart is always expressed as rolling it.

Would it be correct to use везёт here since she is transporting the stroller?

No, везёт (from везти) is used when transporting someone or something in a vehicle. Because the woman is on foot and pushing the wheeled stroller with her hands, катит is the correct verb. If she were transporting the folded stroller in the trunk of her car, then you would use везёт.

Why is the phrase на крутой склон in the accusative case instead of the prepositional?