1) What is Germall Plus?
It is a wide-spectrum antimicrobial preservative commonly used by many home lotion makers. As far as whether it's "natural" or not, I suppose you really mean "is it made in an industrial chemical factory" and the answer is yes, it is. There are no reliable preservatives that are not, even the "Ecocert" preservatives.
Many reputable suppliers sell it -- try LotionCrafter, Majestic Mountain Sage, etc. You'd have to get the product data sheet at their website to get specific info about dosage, limitations, etc.
2) How do I put it into my lotion?
See the product data sheet for specifics. Another reputable source for this kind of information is
http://swiftcraftymonkey.blogspot.ca/
I'm assuming you make lotion with a "heat and hold" method to ensure good emulsification and proper sanitizing. If so, many preservatives, including Germall Plus, must be added during the "cool down" step along with your fragrance and other heat sensitive ingredients. Susan (swift crafty monkey) has detailed info about the "heat and hold" method in her blog and tutorials.
3) Testing shelf life of the lotion - How do I test it? Can I just make it and put it on my shelf in various conditions, then see what happens? Or do I need to send it to some lab?
If you are going to sell the product, you need to have it officially "challenge tested". Just making it and putting it on a shelf is not good enough -- you need to ~challenge~ the product by introducing specific microbial contaminants and see how well they grow in the product.
There are test kits you can purchase from some suppliers (I think LotionCrafter is one) that you can use to test your products on your own, but challenge testing by an independent lab is wise before selling to the general public.
4) I saw that one farm makes 'spray goat milk lotion'. Does anyone have a recipe for that?
I don't have a recipe, but I would start by creating a lotion with a high percentage of water (or water-based ingredients) that would make the lotion thin enough to be sprayed -- the water phase would need to be over 80%, maybe as high as 90%.
Maybe others can chime in with more details, but don't be surprised if you get only suggestions rather than a complete recipe.