Neutrinos are elementary particles of nature, and they are composed of three flavours; electron, muon, and tau neutrinos. Neutrino telescopes, such as the IceCube Neutrino Observatory, detect high-energy neutrinos produced from cosmic ray interactions in the atmosphere and distant astrophysical objects. Such high-energy neutrinos can be used as a probe to search for violations of fundamental spacetime symmetries as new spacetime structure can drive non-standard flavour mixings of neutrinos. Firstly, a search using atmospherically produced neutrinos detected at IceCube is presented. This allows us to set limits on higher-dimensional operators in this framework. Secondly, a search using veryhigh- energy astrophysically produced neutrinos is presented, searching for modifications in the measured astrophysical neutrino flavour composition for the very first time. Although the current statistics and detector sensitivity allows for searches for only rather special new physics effects, it is demonstrated that the sensitivity of this new approach reaches for the first time the necessary precision to look for new physics within the Planck scale expectation. Future neutrino telescopes such as the IceCube-Upgrade will focus on oscillation physics down to few GeV. Here, photomultiplier tubes (PMTs) are used to cover large volumes, however instrumentation is relatively coarse, and particle identification (PID) is done through the morphology of PMT hits. Here, the principle of pulse shape PID using a single 10-inch hemispherical PMT is studied. The Fermilab Test Beam Facility MTest beam line is used to demonstrate that with pulse shape PID, it is possible to distinguish 2 GeV electrons from 8 GeV pions, where the total charge deposition is 20 PE. Furthermore, among the physics of hadronic systems in neutrino interactions, the hadronization model controls multiplicities of final state hadrons. Here, the possibility of implementing the pythia 8 program in the genie neutrino interaction generator is studied, showing comparisons of pythia 8 predictions with neutrino-hadron multiplicity data from bubble chamber experiments.