The word "labor" here refers to working very hard, and "struggle" is a metaphor for dealing with difficulties and dangers. (See: [[rc://en/ta/man/jit/figs-metaphor]])
Paul and his fellow workers confidently expect that God will do all that he has promised to do. Alternate translation: "For we confidently expect that the living God... believers, will do what he promised to do" or "For we fully trust in the living God ... believers"
Possible meanings are 1) "the God who is alive," as opposed to idols, who are not alive, or 2) "God, who acts," as opposed to idols that do nothing, or 3) "God, who gives life to all living beings."
The ellipsis can be filled in. Alternate translation: "but he is especially the Savior of those people who believe" (See: [[rc://en/ta/man/jit/figs-ellipsis]])