The word order for this sentence is confusing. Is there anyway to understand this sentences' word order and if this type repeats somewhere else?
It's a standard word order, similar to:
See the open questions section under 6. in this full explanation.
Is it necessary include the article and say "het middageten," or can you just say "middageten"? What's the difference?
To me personally it sounds awfully strange to say "tijdens middageten". I know in English you don't have to say "during the lunch", though in Dutch it definitely is better to say "tijdens het middageten".
Tijdens het middageten en gedurende het middageten is hetzelfde.
Middagmaal is ook een vertaling voor lunch.