The wavelength of a wave in some medium is reduced, what happens to the period? the velocity? the amplitude? the frequency?

The product of (wavelength) times (frequency) is the speed of the wave
in that particular medium.  So as long as the wave stays in that medium,
that product doesn't change. 

If the wavelength is reduced, then ...

-- the period is reduced by the same factor
-- the frequency is increased by the same factor.

Neither the amplitude of the wave nor its speed in that medium
depends on the wavelength, so they don't change.