Is the relationship between a Muslim and his Lord a self-serving one, where the Muslim performs acts of worship out of fear of God's wrath and desire for Paradise? And did God create humans for their relationships to be based on self-interest, such as a relationship of not exchanging visits or gifts based on that?

The relationship of a Muslim with his Lord is a relationship between a servant who obeys his Master, who created him, provided for him, and bestowed blessings upon him. Allah has the right to command and forbid, and He has the right to be displeased if His servant disobeys Him. The servant's obedience to his Lord is for his own benefit and not for the benefit of the Lord, who is self-sufficient and independent of all His servants. The Lord's promise of Paradise for those who obey Him is a grace and mercy from Him, the Almighty, and an encouragement for the servant, as the servant performs one good deed and Allah multiplies it for him tenfold. The statement that "if you do not bring a gift, the Lord will not guide you, and if you do not visit the sick, He will not visit you" has no evidence from the sacred texts. The Hadith (definition) Qudsi "I was sick, and you did not visit Me" does not mean that if one does not visit the sick, Allah will not visit him.