Paul speaks of the group of believers as if they were a family. Possible meanings are 1) Paul is referring only to Timothy's behavior in the church. Alternate translation: "so that you may know how to conduct yourself as a member of God's family" or 2) Paul is referring to believers in general. Alternate translation: "so that you all may know how to conduct yourselves as members of God's family" (See: [[rc://en/ta/man/jit/figs-metaphor]])
This phrase gives us information about "the household of God" rather than making a distinction between a household of God which is the church and one that is not the church. This can be stated as a new sentence. Alternate translation: "household of God. Those who belong to the family of God are the community of believers in the living God" (See: [[rc://en/ta/man/jit/figs-distinguish]])
Paul speaks of the believers bearing witness to the truth about Christ as if they were a pillar and a base supporting a building. This can be stated as a new sentence. Alternate translation: "which is the church of the living God. And, by keeping and teaching God's truth, these members of the church support the truth just as a pillar and base support a building" (See: [[rc://en/ta/man/jit/figs-metaphor]])