  We study the properties of dark matter haloes in a wide range of modified
gravity models, namely, $f(R)$, DGP, and interacting dark energy models. We
study the effects of modified gravity and dark energy on the internal
properties of haloes, such as the spin and the structural parameters. We find
that $f(R)$ gravity enhance the median value of the Bullock spin parameter, but
could not detect such effects for DGP and coupled dark energy. $f(R)$ also
yields a lower median sphericity and oblateness, while coupled dark energy has
the opposite effect. However, these effects are very small. We then study the
interaction rate of haloes in different gravity, and find that only strongly
coupled dark energy models enhance the interaction rate. We then quantify the
enhancement of the alignment of the spins of interacting halo pairs by modified
gravity. Finally, we study the alignment of the major axes of haloes with the
large-scale structures. The alignment of the spins of interacting pairs of
haloes in DGP and coupled dark energy models show no discrepancy with GR, while
$f(R)$ shows a weaker alignment. Strongly coupled dark energy shows a stronger
alignment of the halo shape with the large-scale structures.
