Using some example sentences, synonyms, and word definitions, here are my suggestions:

"I want more food" - Zu'u laan kip ("I want food" -- "more" is implied because you're asking after eating food). To provide more context - Zu'u laan kip orin mindin pah daar (kip) ("I want food even after all this (food)

"After leaving the field they continued on their journey" - Us bo nol pindaar nust daal wah wundunii ("After leaving from the field they returned to their journey"). To continue a journey is to return to it, because returning can imply continuing an original goal.

"Each warrior is part of the army" -> "The army is built from warriors" - Lahvu wahlaan do kendovve. You convey "part" of something by stating what it is built from/out of.