What is the ruling on the prayer and fasting of someone who has recently embraced Islam and fears his family, and is his fasting valid despite not fulfilling all obligations, and what is incumbent upon him if he misses days of fasting in Ramadan?

Congratulations on the blessing of Islam. Know that Allah does not burden a soul beyond its capacity, as stated in the Quran and Sunnah.

Regarding your acts of worship, if you are unable to perform them fully or openly, then Allah, out of His grace, pardons you. Strive your utmost to fulfill your religious obligations within your capability, without exposing yourself to tribulation. Pray at times that do not attract attention, and if you cannot perform every prayer at its designated time, combine them or make up for the missed ones later.

Similarly, with fasting, fast in a way that does not draw their attention, and make up for any missed fasts whenever possible. If you are unable to do so, then do not burden yourself with what you cannot bear.

Be patient in this situation until Allah grants you relief.