You are welcome!
Well, sometimes. It depends on the oil. Some things are OK to add to a surfactand blend in small amounts without an additional solubilizer, but some oils need Polysorbate 20, and others need Polysorbate 80. The exact composition of FOs can vary greatly and some of them will cloud the base, some won't, some will blend in fine (depending on the surfactants the base is made of - some double as solubilizers) and others won't blend in without an additional solubilizer (either Polysorbate 20, or the FO/EO modifier from WSP). You will have to test each combination to see what happens. If your FO doesn't blend in without a solubilizer, you can try polysorbate 20 or the FO/EO modifier. I would try the polysorbate 20 first, just because it will require less of that than the FO/EO modifier and you won't use up most of your 5% just trying to get the FO to blend in and have no room left for the shea butter.
Here is what I would start with. To your base, add:
2% that is a blend of half FO, half Polysorbate 20
0.5% that is a blend of half Shea butter, and half Polysorbate 80
0.1% or 0.2% Aloe Vera juice
0.2% Vitamin E (acetate form)
That is a total of about 2.9%. You will have some wiggle room in case you need to use the FO/EO modifier instead of Polysorbate 20.
If you add a lot of butter or oil to a surfactant blend, you risk lowering your amount of lather. So if it were me, I would not add any more Shea butter than this. It ends up being about a quarter of one percent, which is probably the same amount as what's in the B&BW formula (if I'm reading their LOI correctly). Think of washing greasy dishes with dish detergent. How much does it lather? Not as much as clean water with detergent, right? When the surfactants are bound up with a lot of oils, instead of free in the water, they can't foam up as much. Also keep in mind that this blend will probably not be clear, but rather cloudy. If that bothers you, try one that is already translucent or opaque.
I recommend getting some test tubes with caps so you can mix up a small batch and let it sit upright in a stand for a week or so, because the tall skinny shape of the test tube will let you see separation much more easily, if it occurs.
Silk amino acids only work in conditioner. Putting proteins in shampoo is more marketing to get people to buy the more exotic products. Surfactants are meant to remove things from hair, so it is difficult to get things to adsorb to the hair strands in the presence of surfactants. If you want to use proteins, you will need to make a leave-in conditioner. Another consideration is the pH. I looked at the SDS for the Crystal Clear Shower Gel and the Pearl Body Wash, and they both have a pH that is quite a bit too high for hair. They are both 6 or above, and shampoo needs to be around 4.5 or 5. It is close enough that you might be able to add a citric acid solution to get it lower, but I do remember seeing in the Q&A for one of them someone asking about lowering the pH, and the WSP employee who answered the question recommended not trying to adjust it (I suspect it will affect viscosity). If you wanted to make a shampoo, you will probably want to start with a base that is only a blend of surfactants (like Iselux Ultra Mild) without all the other stuff, and then add what you want, with the citric acid, your preservative, and thickener. This way you can control the pH much more easily. The nice thing about Iselux Ultra Mild is the viscosity is adjusted by adjusting the pH - lower the pH, and it gets thicker. Or better yet, make shampoo bars instead. 
I did find this on the WSP site: Clear Conditioning Shampoo
That is a shampoo base that might be closer to what you're looking for as a body wash, but the pH is 6.5 which is still quite high for a shampoo, unfortunately. An industry secret is that, frequently the only difference between shampoo and body wash is the label. They are very similar formulations. Typically shampoo can be used as body wash, but sometimes body wash can't be used as shampoo (if the pH is too high). Other than the pH they are basically the same thing. This one looks to me, based on the pH, to be a nice body wash but not so nice as shampoo.
The ingredients of that product are present in the B&BW ingredient list you posted. So it is likely B&BW is using those same ingredients for viscosity control. Keep in mind you still have to stay below 5% total additives. And, don't try to adjust the viscosity until you've let it sit for at least a few days after you get your additives blended in. Sometimes it gets thicker as it sits.
Good idea. I have never ordered from SaveOnScents so I'm unfamiliar with their products. I am pretty familiar with Wholesale Supplies Plus though, and I can tell you that "ship soon" is not a concept they are familiar with, sorry.
I have seen WSP mention it in the Q&A sections. You can probably email it to their customer service email address, although if they take care of that at the same speed they ship things... I've never had to have them calculate it for me because I have only ever bought one base from them, a long time ago, and I didn't sell it. I don't normally use pre-made bases for anything these days so I don't have personal experience with this service. I am merely aware of its existence.
There are actually quite a few things that can get lumped in with "fragrance". 6% fragrance in a body wash is actually really high, so I am pretty certain most of that 6% is a solubilizer of some kind. More like 1% or possibly 2% is actually fragrance.
