On average, your homemade products that include water will last around 3 months. This time depends on how they are stored. Some things have the chance to go “off” in a shorter time period if stored in a warm bathroom environment and if potential contamination is consistently introduced through contact with hands. To increase the shelf-life, they can be stored in the fridge which I understand, isn’t very convenient. Remember, if your product doesn’t include water (like a salve) you don’t need to add a preservative
Both the recipes for the cleanser and the lotion contain natural ingredients to help to keep the products fresh. Keep in mind that vitamin E doesn’t actually stop bacteria or mould from forming in the product. It simply acts as an antioxidant to slow the degradation of the oils, to give them a longer life. Grapefruit seed oil is thought to have more of an ant-microbial effect when added to a product but that alone is not enough of a preservative for retail sale.
There is a wide range of preservatives that natural skincare makers use in their products. This is an area of research that you could really dig into. The preservative you select will depend on various factors such as interactions with other ingredients in your product, cost, solubility, sourcing, and aroma or colour of the preservative! I’d say, for now, experiment with making products for home use and see how long they last for you. Then, you will have a better idea of what you’re looking for in terms of preservation quality.
Through your research, you may find various preservatives that don’t sound “natural.” However, the trusted ones are those that are approved for use in organic skincare products in Canada and the United States.