Q&A: Eid Prayer

When is the time for Eid prayer?

If Eid al-Fitr coincided with the day of Friday, can we pray both Friday and Eid prayers?

I joined the Eid prayers in first Rak`ah when the imam had already said 2 or 3 Takbirs. At that time I was not sure that it’s the first Rak`ah or second, so I made the Niyyah & joined the prayer. Afterwards when the prayer proceeded I came to know that I joined the prayer in the first Rak`ah but had missed around 2 takbirs (& Qunuts). Is the prayer correct or not?

Can an Imam of prayer, lead two separate Eid prayers?

Can one perform Eid prayers, (Eid al-Fitr or Eid al-Adha), at home, by myself, or must I recite these prayers in congregation at the mosque?