There would never be a full moon.
It would fall to Earth's surface.
If the ISS were moving sideways faster than its orbital speed, it would move into a higher orbit or possibly escape Earth's gravity, depending on the speed. It could also potentially enter an unstable orbit that would eventually lead to reentry into the Earth's atmosphere.
If the star is moving in the same direction and at the same speed as Earth, there would be no Doppler shift in the spectrum observed from Earth. The star's light would not be blueshifted or redshifted relative to Earth, since the relative motion is negligible.
It won't; a moving object has the object to continue moving. If one day the Moon mysteriously and suddenly stopped moving around Earth, it would fall upon the Earth pretty soon (in a few days), due to Earth's gravity.
Since everyone and everything on Earth does so anyway, nothing.
it will go same speed forever without affecting mass and weight
Earth's Gravity would pull it straight down to earths surface.
The gravitational pull of the sun would not be balanced by the outward force derived from the Earth's centripetal motion, and the earth would fall into the sun.
It would keep moving at a constant speed in the same direction forever, or until it hits another object.
IF a wave moving at a constant speed were to have it's wavelength doubled (Wavelength x 2), then the frequency of the wave would be half of what it originally was (Frequency / 2).
If the boat is moving upstream at the same speed as the current moving downstream, the boat will appear to be stationary relative to an observer on the shore. This is because the boat's upstream motion is being cancelled out by the downstream motion of the current.
In that case, the Moon would move in a straight line instead of moving around the Earth; it would quickly get away.