This thesis experimentally investigates laser-driven proton acceleration in the regime of target normal sheath acceleration (TNSA) using ultrashort (pulse duration τL = 30 fs), high power (∼100TW) laser pulses. The work focuses on how the temporal intensity profile of the ultrashort laser pulse influences the plasma formation during the laser-target interaction and the subsequent acceleration process. The corresponding experiments are performed at the Draco laser facility at the Helmholtz-Zentrum Dresden – Rossendorf. The main result of the thesis is the experimental observation of transverse spatial modulations in the laser-driven proton distribution. The onset of the modulations occurs above a target-dependent laser energy threshold and is found to correlate with parasitic laser emission preceding the ultrashort laser pulse. The analysis of the underlying plasma dynamics by using numerical simulations indicates that plasma instabilities lead to the filamentation of the laser-accelerated electron distribution. The resulting spatial pattern in the electron distribution is then transferred to the proton distribution during the acceleration process. The plasma instabilities, which the electron current is subjected to, are a surface-ripple-seeded Rayleigh-Taylor or a Weibel instability. Regarding their occurrence, both instabilities show a strong dependence on the initial plasma conditions at the target. This supports the experimentally observed connection between the temporal intensity profile of the laser pulse and the development of spatial modulations in the proton distribution. The study is considered the first observation of (regular) proton beam modulations for TNSA in the regime of ultrashort laser pulses and micrometer thick target foils. The experiments emphasize the requirement for TNSA laser power scaling studies under the consideration of realistic laser-plasma interaction conditions. In that way, the potential of the upcoming generation of Petawatt power lasers for laser-driven proton acceleration can be assessed and fully exploited. In the second part of the thesis, experimental pump-probe techniques are investigated. With an imaging method termed high depth-of-field time-resolved microscopy in a reflective probing setup, micrometer-size local features of the near-critical density plasma as well as the global topography of the plasma can be resolved. The spatio-temporal resolution of the target ionization and heating dynamics is achieved by probing the target reflectivity, whereas the angular distribution of the reflected probe beam carries signatures of the plasma expansion. The presented probing technique avails to correlate the temporal intensity profile of a laser pulse with the spatio-temporal plasma evolution triggered upon laser-target interaction.