Consider the sentence:
I would roughly translate it literally to:
For this trip, in the domain of "total"(abstract location), how many people will be going?"
And then more naturally as:
How many people in total are going on this trip?
My conjecture: で is taking on the role of "location where a verb/event occurs".
(Question 1) What is the role of で for this type of usage?
Other things for your consideration:
JMDict and WWWJDIC categorises 全部 as:
Adverbial Noun (副詞的名詞)(Q1.1),
noun (temporal) (jisoumeishi)(Q1.2)
(Q1.1) But I don't think 全部で acts adverbially to modify the verb 行く. Am I right? (Please correct me if I'm wrong)
(Q1.2) I don't think this part is relevant right? (Again please correct me if I'm wrong)