As the Moon is tidally locked to Earth, that means, from Earth we can only ever see one side of the moon.
Can we see all the sides of the Earth, from the moon?
The Earth and the Moon do interact, but because they have different sizes and masses the effect on each is different.
The Moon rotates once in its orbit around the Earth, causing it to constantly show the same face. This was the Earth's effect on the Moon due to tidal dragging by gravity.
It's pretty stable, the Moon will continue to show the same face to the Earth even as the tidal forces cause it to orbit farther and farther away.
We actually see slightly more than 50% of the Moon. The Moon's orbit causes its aspect to nod because its orbit is slightly elliptical and shimmy because it's not orbiting directly over the equator. Over time we actually see almost 60 percent of the surface of the Moon (an effect called libration).
The Moon's effect on the Earth has been to slow its daily rotation to 24 hours. In the past, the Moon was much closer to the Earth, and the day was much shorter. As time passes and the Moon moves into a wider orbit, the length of the Earth's day will increase (see e.g. this Scientific american post).
I've read that the Moon would recede to a certain point, then begin approaching the Earth again, but unfortunately the Sun will swell into a red giant before then and swallow the Earth and the Moon.
Yes. The tidal locking of the moon with respect to the earth means that the moon rotates once and it axis in exactly the same time it requires to orbit the earth. To always see the same side of earth you have to orbit it in the same time as the earth needs to rotate about its axis, i.e. in 24 hours. The moon orbit around the earth takes about 27 days, so from the moon you'll see the earth rotate below you, and in time you get to see all sides of it.
The orbit period is dictated by the distance from the earth; objects farther from the earth will orbit it more slowly, objects closer by more rapidly. In order to always see the the same side of earth an object needs to be at a particular place, a geostationary orbit, which is in the equatorial plane. This is at 42000 km from the center of the earth, or about 36000 km above its surface.
Television and other communication satellites are in a geostationary orbit, and this orbit is so crowded that satellites sit at just a few tens of kilometers from their neighbors. Everybody wants her satellite at the right longitude to service North America or Europe.
Kepler's 3rd Law says that there's a fixed relationship between the orbital period squared and the distance cubed. For instance the moon's period in days squared is about 750. If you divide the moon's distance cubed by the geostationary orbit's distance cubed you get this same number.