Your adult or matured Aloe plants as shown are just fine planted in the the garden soil that you are using. These are definitely Stockton's variety. Purported to be the best for medicinal qualities. No additions necessary at all.
For your pups in pots you HAVE to use sterilized potting soil for potted plants, any potted plant. There are potting soils designed for succulents/cactus that I would probably use.
Fertilizer should be a simple NPK evenly numbered. I'd use OSMOCOTE 14-14-14 for both potted babies as well as your mature plants. Once or twice per year not their recommended use of every 3 months.
Sterilized potting soil is a solid rule for anything planted in a pot. Don't try adding anything. Some potting soils come with mycorrhizae and bacteria and THAT is just fine. Some potting soils come with added fertilizer, water holding sponges or granules and that is NOT fine. No rocks at the bottom of the soil above the drainage hole! Just soil. Acclimate your baby aloes before transplanting into the garden.
You are assuming the role 'nature' when pots are in play as well in the garden. In the garden you need to add a little decomposed organic matter to feed the micro and macro organisms in your soil. These organisms make a 'live' soil and are necessary to help plants symbiotically to up take chemicals or fertilizer..chemicals YOU are relegated to provide that your plants need to do photosynthesis to make their own food. Wait to give the baby or potted plants fertilizer. Allow them to root well first, then give a bit of fertilizer. There are all kinds of fertilizer formulations just be aware that mulch or compost is not an all purpose fertilizer. Before any fertilization I would acquire a soil test of your garden soil. This will tell you what your soil is lacking or has in abundance. I assume someone else was 'gardening' here before you became owner? Who knows what they added to that soil. Your garden soil looks perfect for these aloes however. 'If it ain't broke don't try fixing it'...
Your crop is beautiful. If you haven't already, I would get a soil test from my nearest Cooperative Extension Service...for cheap. A little fertilizer is great, too much is death. The baby aloes will adapt quickly to the garden soil as long as they are acclimated to the out doors and sun before planting.
As for rocks, in the garden soil, whatever is there is fine. You aren't going to change that soil anytime soon. Soil is little tiny rocks. The size differentiates with different soils; clay is the tiniest flat particles making up soil mixtures, then silt, then the largest particles are sand. All soils are mixtures of these 3 sizes and the percentages make a soil type. Soil types change as one goes down into the subsurface profiles. The other rocks that are in the soil or laying around are going to represent the same as the original rocks that made up your soil.
I only worry about rocks in my garden if they are bigger than my fist otherwise I leave them alone. I am not sure what you meant by your rock question. If the rocks were brought in it is most certainly for 'landscaping'. They have nothing to do with your aloe except to create a 'rock garden'. Those might not be anything like your indigenous rock and soil being brought from different quarries to sell to contractors.
Your plants are happy. Gorgeous, happy aloe plants. I wish I could scoop one up and take it home! Consider your baby aloes in pots as 'starts'. Perfect for gifts or selling at the Farmer's market. Are those flowers yellow?