What is the ruling on praying two rak'ahs before the Eid prayer, and engaging in takbir such as "Allahu Akbar, Allahu Akbar, La ilaha illa Allah, Allahu Akbar wa lillahi al-hamd," and does the ruling differ if the prayer is in the mosque or the Eid prayer ground?

The Sunnah (definition) for someone who comes to the Eid or Istisqa (prayer for rain) prayer ground is to sit and not pray Tahiyat al-Masjid (greeting of the mosque prayer), unless the prayer is held inside a mosque. In that case, one should pray Tahiyat al-Masjid due to the general nature of the Hadith (definition): "When one of you enters the mosque, he should not sit until he prays two rak'ahs." It is prescribed for someone awaiting the prayer to frequently recite "La ilaha illa Allah" (there is no god but Allah) and "Allahu Akbar" (Allah is the Greatest), as these are the شعار (emblem/slogan) of that day.