Galaxy clusters are one of the prime sites to search for dark matter (DM) annihilation signals. Depending on the substructure of the DM halo of a galaxy cluster and the cross sections for DM annihilation channels, these signals might be detectable by the latest generation of $gamma$-ray telescopes. Here we use three years of Fermi Large Area Telescope (LAT) data, which are the most suitable for searching for very extended emission in the vicinity of nearby Virgo galaxy cluster. Our analysis reveals statistically significant extended emission which can be well characterized by a uniformly emitting disk profile with a radius of 3deg that moreover is offset from the cluster center. We demonstrate that the significance of this extended emission strongly depends on the adopted interstellar emission model (IEM) and is most likely an artifact of our incomplete description of the IEM in this region. We also search for and find new point source candidates in the region. We then derive conservative upper limits on the velocity-averaged DM pair annihilation cross section from Virgo. We take into account the potential $gamma$-ray flux enhancement due to DM sub-halos and its complex morphology as a merging cluster. For DM annihilating into $boverline{b}$, assuming a conservative sub-halo model setup, we find limits that are between 1 and 1.5 orders of magnitude above the expectation from the thermal cross section for $m_{mathrm{DM}}lesssim100,mathrm{GeV}$. In a more optimistic scenario, we exclude $langle sigma v ranglesim3times10^{-26},mathrm{cm^{3},s^{-1}}$ for $m_{mathrm{DM}}lesssim40,mathrm{GeV}$ for the same channel. Finally, we derive upper limits on the $gamma$-ray-flux produced by hadronic cosmic-ray interactions in the inter cluster medium. We find that the volume-averaged cosmic-ray-to-thermal pressure ratio is less than $sim6%$.
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