For ANY orbit governed purely by gravity — circular or elliptical — the gravitational force (and hence the acceleration) always points directly toward the central body (Earth's centre); this is the defining feature of motion under a central force, and it holds true throughout an elliptical orbit just as much as a circular one.

The Moon is pulled by BOTH Earth's gravity and the Sun's gravity simultaneously. As seen from the Sun's frame, the total gravitational force acting on the Moon (Earth's pull plus the Sun's) is not purely directed at a single fixed centre — it isn't a simple central force — so the Moon's path around the Sun isn't a strictly, mathematically perfect ellipse, even though it's close to one.

The statement that a line from the Sun to a planet sweeps out equal areas in equal time intervals is Kepler's second law.

In an orbiting satellite, everything (including a pendulum's bob) is in continuous free fall together, so the effective gravity felt inside the satellite is zero. Since a pendulum's period T = 2π√(L/g), as g approaches zero, T approaches infinity — the pendulum simply doesn't swing back and forth at all in this weightless environment.