To simplify things his answer assumes we are working with the case where the mass of the orbiting object is much less than the mass of the object being orbited around. The ideas here are pretty much the same when this is not the case though.
The work done by a force $\mathbf F$ is given by $$W=\int\mathbf F\cdot\text d\mathbf x$$
i.e. the work depends on the component of the force that is in line with the displacement.
In a circular orbit, the gravitational force is always perpendicular to the displacement, so no work is done or is needed to maintain this orbit. All energies remain constant in this case.
What about elliptical orbits? Well certainly kinetic energy of the orbiting object changes throughout the orbit, but this doesn't mean energy is required to maintain the orbit. As the orbiting object moves father away, gravity does negative work and the object slows down. As the orbiting object moves closer gravity does positive work and the object speeds up. Overall energy is conserved though, as the changes in kinetic energy matches the changes in potential energy (work done by gravity).
There is no need for energy to be put be into the system to maintain the orbit.
To explicitly comment on some parts of your post:
I found several answers on this site about the question where gravitational energy comes from
Gravitational potential energy is just a different way to describe the work done by gravity. It doesn't really "come from anywhere", as it's actual value is arbitrary. All that really matters is that a change in gravitational energy means work is being done by gravity (positive or negative). But like my answer above, you don't even need to worry about potential energy. That's why I just talked in terms of work done by gravity.
where does the energy come from that constantly changes the vector of Earth?
Note that a change it velocity vector does not mean work is being done. Only a change in its magnitude (speed) does. Like in the elliptical orbit, gravity doing positive or negative work means the speed of the orbiting object changes. But this doesn't mean the energy "comes from somewhere". Gravity does work, the kinetic energy changes, but the total energy of the system remains constant.