Saying Salam upon entering a house is recommended, not obligatory, regardless of whether anyone is present.

Wudu before sleeping is a recommended Sunnah. If you are still is a state of Wudu from Isha or Tahajjud prayer, then you do not have to renew it.

This is how to get rid of jealousy: make du`a to Allah to rid you of jealousy, ponder the meanings of the Quranic verses on hasad, read about how Prophet Muhammad (peace and blessings of Allah be upon him) kept away from hasad.

This is how to repent in Islam: give up the sin straight away, regret what has happened in the past, resolve not to go back to sinning, restore people’s rights or property, and repent before the agony of death is upon you.

There are many dua`s that you can say to remove depression, anxiety, grief, and sorrow. Read these du`as in the detailed answer.