Context. Theoretical arguments indicate that close-in terrestial exoplanets may have weak magnetic fields. As described in the companion article (Paper I), a weak magnetic field results in a high flux of galactic cosmic rays to the top of the planetary atmosphere. Aims. We investigate effects that may result from a high flux of galactic cosmic rays both throughout the atmosphere and at the planetary surface. Methods. Using an air shower approach, we calculate how the atmospheric chemistry and temperature change under the influence of galactic cosmic rays for Earth-like (N 2 -O 2 dominated) atmospheres. We evaluate the production and destruction rate of atmospheric biosignature molecules. We derive planetary emission and transmission spectra to study the influence of galactic cosmic rays on biosignature detectability. We then calculate the resulting surface UV flux, the surface particle flux, and the associated equivalent biological dose rates. Results. We find that up to 20% of stratospheric ozone is destroyed by cosmic-ray protons. The effect on the planetary spectra, however, is negligible. The reduction of the planetary ozone layer leads to an increase in the weighted surface UV flux by two orders of magnitude under stellar UV flare conditions. The resulting biological effective dose rate is, however, too low to strongly affect surface life. We also examine the surface particle flux: For a planet with a terrestrial atmosphere (with a surface pressure of 1033 hPa), a reduction of the magnetic shielding efficiency can increase the biological radiation dose rate by a factor of two, which is non-critical for biological systems. For a planet with a weaker atmosphere (with a surface pressure of 97.8 hPa), the planetary magnetic field has a much stronger influence on the biological radiation dose, changing it by up to two orders of magnitude. Conclusions. For a planet with an Earth-like atmospheric pressure, weak or absent magnetospheric shielding against galactic cosmic rays has little effect on the planet. It has a modest effect on atmospheric ozone, a weak effect on the atmospheric spectra, and a noncritical effect on biological dose rates. For planets with a thin atmosphere, however, magnetospheric shielding controls the surface radiation dose and can prevent it from increasing to several hundred times the background level.