The planets revolve around their star because of the gravitational force that holds them close to the star, in very stable orbits, but not immutable.

We must answer the question: no, the Earth does not move away from the Sun. For that, according to the laws of physics, it would be necessary that its speed of revolution increases, therefore that an external force is applied to it.

But, the orbit of the Earth can change shape under the gravitational influence of other planets.

We see that the gravitational attraction between two objects (a planet and its star, for example), depends on two things: the masses of the two objects and the distance that separates them. The greater the masses, the stronger the attraction, but the greater the distance, the weaker the attraction.

It is possible to compare the dimensions of the planets and the Sun. The Sun is immensely large compared to the Earth (and the other planets); no wonder the motion of the Earth is mainly governed by this huge mass.

And if we start from the left of the picture, the Earth is the third planet. And the fourth is Mars. You can see that it is smaller. In fact, Mars is only 10% of the mass of the Earth. So even when the Earth is between the Sun and Mars, the tiny attraction due to the red planet is completely negligible compared to the huge attraction of the Sun.

The planet Venus is the second planet. Almost as big as the Earth, it does have an influence on our orbit. Every time we come close to it, Venus modifies our orbit a little. And we modify its orbit.

As for Jupiter, even if it is farther away, the fifth planet has a much larger mass than Mars. As a result, it has an influence on our orbit too.

Anyway, to answer the second question, Mars is too small for its gravitational attraction to have any influence on the trajectory of our planet.

The influences of Venus and Jupiter do not move the Earth into orbits closer or farther from the Sun. They only slightly modify the shape of the orbit, more elliptical or more round.