Thousands.
See related link for a picture.
Please update this answer with the amount you have counted.
Because the near side is protected somewhat by the earth.
yes
There can be craters anywhere on the moon, not just the side we see
Almost all the maria are on the near side. The far side is mostly just craters.
The moon has a geosynchronous rotation as it orbits the earth, meaning the same side of the moon always faces the earth. The side we don't ever see from earth is known as the "far" side of the moon. The far side has more craters because it is not protected from debris by the earth.
The "darkside" or the part of the Moon that does not face the Earth has the most craters.
The near side of the Moon is the one we see; maria (seas), highlands, craters, and mountains. The far side is much different. The far side is more mountainous, with fewer obvious craters and very few plains or flat areas.
Craters.
The number of craters on the moon are too many to count. Approximately 300,000 craters with diameters of 1 km or more are visible from ground based telescopes. High-definition photographs from lunar probes reveal millions of craters. Extreme closeups show countless microscopic craters.
The Moon's crust may be thicker on the far side. So there was less volcanic activity. So there is less lava to cover up craters. Lava flows form the "maria" which are much more in evidence on the side facing Earth.
There are two separate things that need to be addressed. One is the surface area of the Moon. The other is the surface area of the NEAR SIDE of the Moon. As a sphere in space, the Moon is always 50% illuminated, except during lunar eclipses. The phases of the Moon measure what percentage of the NEAR SIDE of the Moon is illuminated. At the new moon, none of the near side is lit up; at the full moon, 100% of the near side is illuminated.
Mercury looks a lot like the far side of the moon. It is lifeless and littered with countless craters.