We consider the business parts of the team to be (pretty much) anything involving money, mostly everything that you posted. I'll start explaining how we(CRT) deal with these aspects in order of your list:
-Ordering parts is done by one of the student leaders, The design team sees exactly what is needed, and the student that is most involved in the design at that point of build writes up a list of what to order and either gives that to our main mentor, or calls up the company them self. The money for the parts comes out of the team fund, and is hopefully reimbursed by the high-school administration before too long.
-Travel arrangements on our team used to be made by a few of the students, but do to them graduating, we are at a loss for students who are interested in This aspect of the team. Because of this, our main mentor, Ken Morrison takes care of it for us. (Thanks Mr. Morrison
) The money situation is almost the same as for ordering parts, but I am not sure of the details yet... I will be in a couple of months
-At the competitions, we either eat as a group (each student is expected to keep the cost of their meal reasonably low), or each student is given an amount to go eat on their own. As far as I know, We are reimbursed for every penny spent on food.
-Registration is solely taken care of by Mr. Morrison, and I am not sure if we are reimbursed on it.
Despite how much money we receive from the school district, we have year round fund-raisers, Mr. Morrison has a candy store setup in his classroom and all of the profit goes into the robotics fund, he also lathes his own (Very nice) pens and mechanical pencils out of wood and other assorted materials such as dear antlers,which sell for about 15 dollars each with cases. We also have a two week fundraiser done by the students each year.
Sorry there are so many blank spots in my knowledge, but I'm trying to fill them in as best as I can... And I hope this response was along the lines of what you were looking for