Electronic – Why do the satellite manufacturing companies themselves make their crystals

The main reason is that a 1 Hz crystal would have to be physically very big. A crystal is a piece of quartz that mechanically vibrates at the specific frequency. Since quarts exhibits a fairly strong piezo-electric effect, those vibrations also cause electrical signals and vice versa.

Getting a physically small crystal down to 33 kHz resonant frequency was quite a breakthru not that long ago. The trick is to shape the quartz like a tuning fork. That allows for much slower oscillations than a solid block of quartz of the same size. However, extending that another 3½ orders of magnitude is going to make the crystal a lot bigger.

It's hard to imagine what use a 1 Hz crystal would be, considering how cheap and easy it is to start with a faster frequency and then divide down with a counter. 33 kHz is already so slow that you won't get any significant power savings by running the logic any slower. In fact, filtering the harmonics from a 1 Hz square wave and still providing the drive for the size crystal that it would take to make that frequency would take significantly more power. It just doesn't make sense. Put another way, a 33 kHz crystal with its drive circuit and a digital counter is smaller, cheaper, and takes less power than a 1 Hz crystal with the drive circuitry it would require.

You are actually building an oscillator circuit, using a crystal, some capacitors, and the internal circuitry of your microcontroller. If you don't use the caps, your clocking won't work. The values are calculated based on the properties of the crystal, as described in http://ww1.microchip.com/downloads/en/appnotes/00826a.pdf, page 9

Essentially, the load capacitance of the crystal, \$C_L\$, is set equal to the combination of the capacitors you're adding and the shunt capacitance of the crystal, so

$$ C_L = \frac{C^2}{2C} + C_{shunt} $$

The ppm figures specify the (in)accuracy of the crystal (when properly used): 5 ppm is 5 parts per million.

Second and third overtones involve driving the crystal into resonance at a harmonic. I suggest not trying this.