"Our group eats lunch with the children."
Translation:Unsere Gruppe isst mit den Kindern Mittagessen.
After "mit", you have to use the dative case. In the dative plural, all words add an additonal "-n" or "-en":
Ex. "die Kinder" (the children, nominative plural) becomes "mit den Kindern" (with the children, dative plural).
The only exceptions are words whose nominative plural already ends in "-n" (e.g. Frauen) and words whose nominative plural ends in "-s" (e.g. Autos).
No, it's not correct. In a "normal" sentence, i.e. not a question or a subordinate clause such as "because our group eats lunch", the inflected verb has to be the second element.
Unsere Gruppe (= 1st element) isst (=2nd element) ...
Also, it's "unsere", not "usere" (spelling).
"Gruppe" is feminine singular and the subject of the sentence (= nominative case). Therefore, the form of "unser" you have to use must be feminine, singular, nominative as well: unsere
See this chart (it's for "mein", but the endings are the same):
"Unsere Gruppe" (our group) is singular. The plural would be "unsere Gruppen" (our groups).
As "Gruppe" is grammatically singular, it is treated as such in German and the verb that belongs to "Gruppe" is singular as well. The same goes for other singular nouns such as "die Mannschaft" (the team), "die Partei" (the [political] party), etc. That's a difference to - esp. British - English.
In some contexts, you can use "Gruppe" with a plural verb, but only if it is combined with a plural noun, e.g. "eine Gruppe von Kindern" (a group of children). Duden, the most important German dictionary, says that using a plural verb is acceptable in these cases but recommends using a singular verb even here.