Yes, the antenna is half wave. Usually the optimum value for the overall length is a bit shorter than 0.5*wavelength.
In this case I used the free program MMANA-GAL to design the antenna. It predicts the best overall length to be 32.6 cm (tip to tip)
The cheap receivers (superregenerative) are fine, but of course the slightly more expensive superheterodyne receivers will be a bit more sensitive.