For propagating loquats, pomegranates, and guava, you can indeed use young branch cuttings. This method allows the new plants to retain the fruit quality of the original tree. The process generally involves selecting healthy cuttings, preparing them (such as by dipping in rooting hormone), and planting them in suitable conditions for rooting. Pomegranates, for example, can be propagated from 6-inch-long cuttings taken from mature plants during late winter. These cuttings should be prepared by removing some leaves and possibly using rooting hormone, then planted in nutrient-rich potting soil.
As for your second question, using rootstock shoots or cuttings from below the graft of deciduous plants like Asian pear trees is a feasible method to create new rootstock plants. Rootstocks are often propagated this way, though they can also be grown from seeds. Each method has its own advantages and considerations, so it might be beneficial to experiment with both to see which yields the best results for your specific conditions and needs.