Traffic fatalities remain among the leading death causes worldwide. To reduce this figure, car safety is listed as one of the most important factors. To actively support human drivers, it is essential for advanced driving assistance systems to be able to recognize the driver's actions and intentions. Prior studies have demonstrated various approaches to recognize driving actions and intentions based on in-cabin and external video footage. Given the performance of self-supervised video pre-trained (SSVP) Video Masked Autoencoders (VMAEs) on multiple action recognition datasets, we evaluate the performance of SSVP VMAEs on the Honda Research Institute Driving Dataset for driver action recognition (DAR) and on the Brain4Cars dataset for driver intention recognition (DIR). Besides the performance, the application of an artificial intelligence system in a safety-critical environment must be capable to express when it is uncertain about the produced results. Therefore, we also analyze uncertainty estimations produced by a Bayes-by-Backprop last-layer (BBB-LL) and Monte-Carlo (MC) dropout variants of an VMAE. Our experiments show that an VMAE achieves a higher overall performance for both offline DAR and end-to-end DIR compared to the state-of-the-art. The analysis of the BBB-LL and MC dropout models show higher uncertainty estimates for incorrectly classified test instances compared to correctly predicted test instances.