If a wave train of 10,000 waves covers 100cm, what is true? Are we talking about calculating the wavelength, frequency, wave number or period? Why?

We would be talking about the wave number, sometimes referred to as wavenumber.  The wave number is the space frequency of the wave, specifically number of cycles per unit of distance or radians per unit of distance.  If we had 10,000 waves covering a distance of 100 centimeters, that would be expressed as 10,000 waves/100 centimeters.  When you divide, you get a wave number of 100 cycles per centimeter.

In contrast, the frequency of a...

We would be talking about the wave number, sometimes referred to as wavenumber.  The wave number is the space frequency of the wave, specifically number of cycles per unit of distance or radians per unit of distance.  If we had 10,000 waves covering a distance of 100 centimeters, that would be expressed as 10,000 waves/100 centimeters.  When you divide, you get a wave number of 100 cycles per centimeter.

In contrast, the frequency of a wave involves a time element, such as how many waves pass a fixed point per second, per minute, or per hour.  The wavelength measures the specific length from one crest to the next consecutive crest, or trough to trough.  The period requires an element of time again, specifically the time required for a wave cycle to complete passage by a fixed point.  Out of all these, the wave number is the correct choice, as it involves a specific number of waves passing over a specific distance.