What is the ruling on performing Tarawih in sets of four rak‘ahs with only one Tasleem?

It is not permissible to combine more than two rak‘ahs with a single Tasleem in Tarawih prayer. Whoever does so, their prayer is invalid. Shaykh al-Islam Imam Muhammad al-Ramli (may Allah have mercy on him) stated: "If a person prays four rak‘ahs of the Tarawih prayer with a single Tasleem, it is not valid if they did so intentionally and with knowledge [of the prohibition]. Otherwise, it becomes an 'absolute voluntary prayer' (nafl mutlaq); because it is contrary to what has been prescribed." [Nihayat al-Muhtaj, Vol.2/P.127].

Is it permissible to offer mandatory prayer while sitting?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.                                                                                                                                                                                                                            Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.

Does passing wind, from the anus without a smell, invalidate prayer?

If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.

If someone fasts on the White Days with the intention of making up for missed fasts (qada), will they receive the reward for both voluntary and obligatory fasting?