1. Qiyam al-layl means spending the night, or part of it, even if it is only one hour, in prayer, reading Quran, remembering Allah (dhikr) and other acts of worship. 2. Tahajjud means specifically praying at night, and some scholars limited it to prayers that are offered at night after sleeping. 3. Taraweeh refers to qiyam al-layl in Ramadan at the beginning of the night, which should be made light and not lengthy. It may also be called tahajjud or qiyam al-layl.

Praying Tarawih in congregation in the mosque is better than praying at home. This is indicated by the Sunnah and the actions of the Companions (may Allah be pleased with them).

Taraweeh prayer is a recommended Sunnah and comes under the heading of qiyam al-layl. Whoever prays Tarawih in Ramadan out of faith and in the hope of reward, his previous sins will be forgiven.

If you recite Qunut in Witr prayer every night, there is nothing wrong with that. And if you omit it on some occasions so that the people will know that it is not obligatory, there is nothing wrong with that either.