Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
What is the ruling on insulin injections?
Insulin injections do not break the fast because they are administered under the skin and do not reach the body cavity (jauf).
What is the ruling of Islamic Law on continuity (muwalah) in the ritual bath?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Continuity (muwālāh) means washing each part of the body immediately after the previous one, without leaving a gap long enough for the first part to dry before the second is washed. According to the Shāfiʿī school, continuity is a recommended act (sunnah) in both the ritual bath (ghusl) and ablution (wuḍūʾ) — it is not obligatory.
It is stated in Nihāyat al-Muḥtāj ilā Sharḥ al-Minhāj: "Likewise, continuity in the ritual bath is recommended, just as it is in ablution."
Accordingly, continuity in the ritual bath is a sunnah. And Allah the Almighty knows best.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.