It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that Allah Almighty said: "So perform tahajjud with it as an extra (nafilah) for you." [Surah al-Isra: 79] That is, voluntary prayer: standing in prayer at night (qiyam al-layl) was made specific to him (peace and blessings be upon him), and it is obligatory on him.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 13271
The Prophet (peace and blessings be upon him) said: "There are three things that are obligatory for me and sunnah for you: witr, the tooth-stick (miswak), and standing in prayer at night."
This Musa bin Abd al-Rahman is very da'if (weak), and no chain on this is established. And Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 13272
It is narrated from Sayyiduna al-Mughirah bin Shu'bah (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) would pray until his blessed feet became swollen. This was mentioned to him, and he (peace and blessings be upon him) said: "Should I not be a grateful servant of Allah?"
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 13273
Sayyidah Aishah (may Allah be pleased with her) said: When the Prophet (peace and blessings be upon him) prayed, his blessed feet would swell. Sayyidah Aishah (may Allah be pleased with her) said: O Prophet of Allah! Why do you do this, when Allah has forgiven your past and future sins? He (peace and blessings be upon him) said: "O Aishah! Should I not be a grateful servant of Allah?"
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 13274