1 which body contains the majority of the mass in the solar system

earth

Jupiter

the moon

the Sun

2 what keeps the objects in the solar system such as planets orbiting around the Sun

the force of gravity the Galaxy exerts on all objects within it including the solar system

the great distance between the Sun and the planets

the sun's nuclear fusion which acts on each object

the gravitational force between the Sun and each object in the solar system

the answer to one is the sun the answer to two is the last option

1). Of everything that makes up the entire solar system ... the Sun, eight major planets, more than a hundred moons, bunches of dwarf planets, all of the asteroids, huge quantities of asteroids, comets, and meteoroids, millions of Kuiper Belt objects, millions of Oort Cloud objects ... if you add up the mass of EVERYthing, the Sun has more than 99% of all the mass, and everything else has less than 1% of it.

2). The gravitational force between the Sun and each object in the solar system keeps the object in orbit around the sun.

- - Also, the gravitational force between a planet and each of its moons keeps that moon in orbit around that planet.

- - Also, the gravitational force between the Earth and the ISS, and between the Earth and every TV satellite or weather satellite, keeps each of those objects in orbit around the Earth.