To find out what frequencies a signal contains you Fourier transform it.
If you have an infinite plane wave, $\psi$, then when you Fourier transform it you get a delta function centred on the wave frequency i.e. it contains a single frequency.
However a wave packet of the type shown is the product of an infinite plane wave, $\psi$, and some envelope function, $E$, e.g. a Gaussian. When you Fourier transform this product the frequency distribution you get is the Fourier transform of $\psi$ convolved with the Fourier transform of $E$. $\psi$ tranforms to a delta function but, assuming it's a Gaussian, $E$ transforms to another Gaussian. The convolution of the two gives a Gaussian i.e. the packet contains a range of frequencies not just a single frequency.
It's because the packet contains a distribution of frequencies that you can't assign it a definite frequency/wavelength. The best you can do is assign an average frequency.
Re the uncertainty in position: the position is given by the envelope function, $E$, as described above. In effect $E$ tells you the probability of finding the particle at some position/time. To get a precise position you need to shrink $E$ to a delta function, but if you do that you find it's Fourier transform goes to a constant i.e. the packet now has an infinitely uncertain frequency and therefore momentum.