بسم الله الرحمن الرحيم
(1) No musafaha (shaking hands) and muaanqa (hugging) is proved from Shariah after Eid salah; hence it is bida’h to do musafaha and muaanqa considering it sunnah after Eid salah. It shall earn you sin instead of reward. However, it is lawful to say Eid Mubarak when the moon is sighted.
(2) It is not proved from the Sahaba etc to visit elders after Eid salah on Eid day to say Eid Mubarak hence it shall not be correct to consider it sunnah.
(3) The following practices are sunnah on Eid day; each Muslim should do them: (1) To take a bath. (2) To do miswak. (3) To put on one’s best clothes. (4) To apply attar. (5) To take any sweet before going for Eid salah. (6) To pay sadaqah fitr before Eid salah if it is wajib. (7) On the occasion of Eid al-Azha not to eat anything before the salah and eat the meat of Qurbani after salah. (8) To perform Eid salah in Eidgah. (9) To go to the Eidgah by foot i.e. should not ride unnecessarily. (10) To go by one route and return by another one. (11) Not to perform any nafl salah at home or Eidgah before Eid salah and not offering any nafl in Eidgah after Eid salah. However you may offer nafl salah when you reach home. (12) To say Takbeer Tashriq while going to the Eidgah, however it shall be read in low voice during Eid al-Fitr and aloud Eid Al-Azha. Here is the Takbeer Tashriq:
الله أكبر، الله أكبر، لا إله إلا الله، والله أكبر، الله أكبر ولله الحمد .
(13) To express cheerfulness and happiness. (14) To do sadaqah extensively. So it is mentioned in the books of Fiqh and Fatawa.
Allah knows Best!
Darul Uloom Deoband