Breakdown of butyou ha kaigityuu ni koohii wo nomimasu.

Questions & Answers about butyou ha kaigityuu ni koohii wo nomimasu.
会議中 by itself means “during the meeting,” but when you want to use it as a time expression, you usually add に to mark “at/during that time.”
You can sometimes omit に after 〜中 (e.g. 会議中コーヒーを飲みます), but including に makes the time-marker explicit and sounds more natural in polite statements.
Both mean “during the meeting.”
• 会議中 uses the suffix 中 attached directly to 会議, making it concise.
• 会議の間 uses 間 (“interval”) with the possessive の, literally “the interval of the meeting.”
Usage-wise they’re interchangeable, though 会議中 is more common in everyday speech.
Yes.
• 部長は会議中にコーヒーを飲んでいます。
This indicates that the manager is in the process of drinking coffee right now during the meeting, rather than describing a habitual behavior.
Yes, Japanese word order is relatively flexible. Both of these are grammatical:
1) 部長は会議中にコーヒーを飲みます。
2) 部長はコーヒーを会議中に飲みます。
However, putting the time expression 会議中に before the object often sounds clearer and more natural, because it sets “when” before “what.”