  When subjected to parallel electric field $\mathbf E$ and magnetic field
$\mathbf B$, Weyl semimetals exhibit the exotic transport property known as the
chiral anomaly due to the pumping of electrons between Weyl cones of opposite
chiralities. When one or both electromagnetic (EM) fields are replaced by
strain-induced chiral pseudo-electromagnetic (pseudo-EM) fields, other types of
quantum anomalies occur. In the present paper, we will show that such quantum
anomalies can be reproduced in a completely different system -- a Weyl
ferromagnet whose magnonic structure remarkably encodes Weyl physics. By
analytical and numerical calculations, we will show that the magnon bands can
be Landau-quantized by either an inhomogeneous electric field $\mathbf E$ or a
chiral pseudo-electric field $\mathbf e$ induced by a torsional strain, and
magnons can be pumped along bands by either an inhomogeneous magnetic field
$\mathbf B$ or a chiral pseudo-magnetic field $\mathbf b$ due to a dynamic
uniaxial strain. We list the magnon quantum anomalies and the associated
anomalous spin and heat currents in the Weyl ferromagnet, and show they are
distinct from their Weyl semimetal counterparts.
