This thesis presents several experiments, generally aiming at visualising the ballistic and topological transport on the high-mobility graphene/boron nitride heterostructure using the scanning gate microscope. For the first experiment, we use the scanning gate microscopy to map out the trajectories of ballistic carriers in high-mobility graphene encapsulated by hexagonal boron nitride and in a weak perpendicular magnetic field. We employ a magnetic focusing transport configuration to image carriers that emerge ballistically from an injector, follow a cyclotron path due to the Lorentz force from an applied magnetic field, and land on an adjacent collector probe. The local potential generated by the scanning tip in the vicinity of the carriers deflects their trajectories, modifying the proportion of carriers focused into the collector. By measuring the voltage at the collector while scanning the tip, we are able to obtain images with arcs that are consistent with the expected cyclotron motion. We also demonstrate that the tip can be used to redirect misaligned carriers back to the collector. For the second experiment, we investigate the graphene van der Waals structures formed by aligning monolayer graphene with insulating layers of hexagonal boron nitride which exhibit a moir$e´$ superlattice that is expected to break sublattice symmetry. However, despite an energy gap of several tens of millielectronvolts opening in the Dirac spectrum, electrical resistivity remains lower than expected at low temperature and varies between devices. While subgap states are likely to play a role in this behaviour, their precise nature is still unclear in the community. We therefore perform a scanning gate microscopy study of graphene moir$e´$ superlattice devices with comparable activation energy but with different charge disorder levels. In the device with higher charge impurity ($\sim$ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">10</mrow>}$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$) and lower resistivity ($\sim$ 10 k$\Omega$) at the Dirac point we observe scanning gate response along the graphene edges. Combined with simulations, our measurements suggest that enhanced edge doping is responsible for this effect. In addition, a device with low charge impurity ($\sim$ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">9</mrow>}$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$) and higher resistivity ($\sim$ 100 k$\Omega$) shows subgap states in the bulk. Our measurements provide alternative model to the prevailing theory in the literature in which the topological bandstructures of the graphene moir$e´$ superlattices entail an edge currents shunting the insulating bulk. In the third experiment, we continue our study in the graphene moir$e´$ superlattices with the newly reported non-local Hall signals at the main Dirac point. It has been associated with the non-zero valley Berry curvature due to the gap opening and the nonlocal signal has been interpreted as the signature of the topological valley Hall effects. However, the nature of such signal is still disputed in the community, due to the vanishing density of states near the Dirac point and the possible topological edge transport in the system. Various artificial contribution without a topological origin of the measurement scheme has also been suggested. In connection to the second experiment, we use the scanning gate microscope to image the non-local Hall resistance as well as the local resistance in the current path. By analysing the features in the two sets of images, we find evidence for topological Hall current in the bulk despite a large artificial components which cannot be distinguished in global transport measurement. In the last experiment, we show the development of a radio-frequency scanning impedance microscopy compatible with the existing scanning gate microscopy and the dilution refrigerator. We detailed the design and the implementation of the radio-frequency reflectometry and the specialised tip holder for the integration of the tip and the transmission lines. We demonstrate the capability of imaging local impedance of the sample by detecting the mechanical oscillation of the tip, the device topography, and the Landau levels in the quantum Hall regime at liquid helium temperature and milli-Kelvin temperature.