  We have obtained the Generalized Uncertainty Principle (GUP) corrected de
Sitter and anti-de Sitter black hole solutions in bumblebee gravity with a
topological defect. We have calculated the scalar, electromagnetic and
gravitational quasinormal modes for the both vanishing and non-vanishing
effective cosmological constant using Pad\'e averaged sixth order WKB
approximation method. Apart from this, the time evolutions for all three
perturbations are studied, and quasinormal modes are calculated using the time
domain profile. We found that the first order and second order GUP parameters
$\alpha$ and $\beta$, respectively have opposite impacts on the quasinormal
modes. The study also finds that the presence of a global monopole can decrease
the quasinormal frequencies and the decay rate significantly. On the other
hand, Lorentz symmetry violation has noticeable impacts on the quasinormal
frequencies and the decay rate. We have studied the greybody factors, power
spectrum and sparsity of the black hole with the vanishing effective
cosmological constant for all the three perturbations. The presence of Lorentz
symmetry breaking and the GUP parameter $\alpha$ decrease, while other GUP
parameter $\beta$ and the presence of global monopole increase the probability
of Hawking radiation to reach the spatial infinity. The presence of Lorentz
violation can make the black holes less sparse, while the presence of a global
monopole can increase the sparsity of the black holes. Moreover, we have seen
that the black hole area quantization rule is modified by the presence of
Lorentz symmetry breaking.
