In the field of medical ultrasound imaging, conventional B-mode ``grey scale'' ultrasound and shear wave elastography (SWE) are widely used for chronic liver disease diagnosis and risk stratification. However, many abdominal ultrasound images do not include views of the liver, necessitating a pre-processing liver view detection step before feeding the image to the AI system. To address this, we propose a self-supervised learning method, SimCLR+LR, for image classification that utilizes a large set of unlabeled abdominal ultrasound images to learn image representations. These representations are then fine-tuned to the downstream task of liver view classification. This approach outperforms traditional supervised learning methods and achieves superior performance when compared to state-of-the-art (SOTA) models, ResNet-18 and MLP-Mixer. Once the liver view is detected, the next crucial phase involves the segmentation of the liver region, imperative for obtaining accurate and dependable results in SWE. For this, we present another self-supervised learning approach, SimCLR+ENet, which leverages the learned feature representations and fine-tunes them on the task of liver segmentation, followed by a refinement step using CascadePSP. The proposed approach outperforms the SOTA method U-Net. SimCLR+ENet was also used to detect poor probe contact (i.e., areas where the ultrasound probe/transducer does not have adequate contact with the patient's skin) in liver ultrasound images, an artifact that affects the reliability of SWE. The combination of the proposed self-supervised learning methods for liver view classification, liver segmentation, and poor probe contact detection not only reduces the time and cost associated with data labeling, but also optimizes the liver segmentation workflow and SWE reliability in a real-time setting.