Is it permissible to say "Alhamdulillah (Praise be to Allah)" in response to "How are you?" even if one is tired or distressed, and to say "Nothing" in response to "What troubles you?" in order to avoid saddening the questioner or for fear of losing reward?

It is permissible for a Muslim to praise God when asked about their condition, and it is recommended to frequently praise God in times of ease and hardship, because "the best of God's servants on the Day of Resurrection are those who praise Him excessively," and "the first to be called to Paradise are those who praise God in times of ease and hardship." When the Prophet, peace and blessings be upon him, saw something he liked, he would say: "Praise be to God, by whose grace good deeds are perfected," and when he saw something he disliked, he would say: "Praise be to God in every circumstance."

There is no harm in disclosing one's condition, whether it be worry or illness, as long as it is not a complaint or an expression of discontent with God's decree, because "whoever is content will find contentment, and whoever is displeased will find displeasure." However, concealing it and praising God is more virtuous, especially to preserve the reward for patience or to avoid distressing others. Part of perfect patience is concealing illness.

There is no harm in saying "nothing" to someone who asks about worry or fatigue, as this falls under the category of dissimulation.