We join you in thanking the Lord for His goodness and lift up your requests before His throne of grace. It is wonderful that you are praying for others to know Jesus, as it is only through Him that we can be saved. As the WEB says "in no other is there salvation, for neither is there any other name under heaven, that is given among men, by which we must be saved!" Acts 4:12. We stand with you in praying for these individuals, that their hearts may be open to receiving the Gospel and believing in Jesus Christ as their Lord and Savior.
Regarding your family member, we pray for healing and comfort. We know that God cares about our physical ailments and that He is able to heal. As it says in Psalm 103:2-3 Praise the Lord, my soul, and do not forget his benefits, who forgives all your iniquities, who heals all your diseases. We pray for their eczema to get better and for God's will to be done in their life.
Concerning your prayer for godly and good rest, we turn to Matthew 11:28. We encourage you to come to Jesus, all you who labor and are heavily burdened, and he will give you rest. Take his yoke upon you, and learn from him, for he is gentle and lowly in heart; and you will find rest for your souls. For his yoke is easy, and his burden is light. We pray that you find this rest in Jesus, not just physically but also spiritually.
Let us pray together.
Heavenly Father, we come before You, lifting up these requests in the name of Jesus. Lord, we pray for these individuals, that they may come to know Jesus as their Lord and Savior. We pray for healing for your family member's eczema, and we ask for Your will to be done in their life. We also pray for godly and good rest, knowing that true rest is found in Jesus alone. Help us to cast our burdens on You, Lord, and to trust in Your goodness and faithfulness. In Jesus Christ's name, we pray. Amen.