I intended to include a promise at the end of the original post about the certainty of a follow-up. I forgot to include that line, but here it is anyway.
I am staying in NHS. I asked the coordinator (in a strictly nonconfrontational way) my questions and got satisfactory answers.
First, the membership fee is nothing new. Apparently, the membership fee and the second (spring) Cookie Dough sale are needed to cover operating costs, and even then, we barely keep any of the money.
Second, there is no requirement to actually bring a friend to the Mini-Walk. The only requirement is that said friend pay the same fee to participate. Bringing a friend is just strongly encouraged, but there is no punishment (explicit or otherwise) for not doing this.
Next, I got the impression that the coordinator and the professional liaison only wanted focus on money rather than the actual target of charity. This is because the target actually isn't specific. The first (fall) Cookie Dough sales will go through KenyaConnect (as it always has) to go to villages in Kenya. Last year, they could give specifics because conditions were alright to commit to specific projects (i.e. school chairs and tables, water tanks, gates and fences). This year, with the drought and famine (for the last 8 months) in Kenya, it is still unclear to even KenyaConnect as to how exactly the money will be allocated. That's why the focus was more on actually raising the money itself.
Finally, I did not get a chance to ask about Windows on used computers, but I plan to later on.
Also, some other things that the NHS does is help out with the Children's Inn at NIH, various senior nursing homes, and other things.
This all is enough to convince me that the NHS is a (mostly) charitable fundraising organization, and that's enough to make me stay.