Your questions pertain mostly to cosmeti formulation rather than perfumery. Since I have experience with cosmetic formulation I'll help as I can.
The odourless carrier oil Is jojoba, a liquid wax with an indefinite shelf life. Fractioned coonut oil ( capric\caprilyc triglyceride) or mineral oil.
EO's for direct application to the body can be anything from 1-10%.
In order to mix oil and water you need an emulsifier, the polysorbates are emulsifiers.
Glycerin is a humectant commonly used in cosmetics, it makes the skin feel moisturised. A body mist of oil, water and glycerin won't feel very nice and will possibly be slick or sticky depending on ratios. Better skin feel with be achieved by adding a silicone. Most commercial body mists are mineral oil and silicone based.
Your best bet for help with body product formulations and how to do it is the EDS Forum, DIY section. You will also find suppliers of all these products recommended there as well. This site is focused on making perfumes in alcohol like the commercial ones and how to formulate scents.