In those communities where the masjids have not yet opened, Ṣalāt al-Eid should be prayed in one’s houses with one’s own family, and there is no need for a khuṭbah.
The Eid prayer is not the same as the Friday prayer, as Friday prayer has different conditions and rulings. While the general rule is that Eid ṣalat should be prayed in a large congregation, it is permissible even in regular circumstances for the one who missed Eid ṣalat to make it up at home. The servant of the Prophet (saw), Anas b. Mālik (r ) once missed the Eid prayer in Basrah, so he gathered his family and had one of his household lead them in two rak’ats. And Aṭāʿ b. Abī Rabāḥ (d. 114 AH) said regarding the one who missed the Eid prayer, “Let him pray two rak’ats and say the takbīrs”. Hammād b. Abī Sulayman (d. 120 AH), the famous scholar of Kufa and teacher of Abu Ḥanīfa, said when asked the same question, “He should pray as they prayed, and do the takbīrat as they did” [These reports are in the Muṣannaf of Ibn Abī Shaybah, 2/4-5]. All of these reports are regarding those who missed Eid for any reason. Notice that the Friday prayer would not be ‘made up’ like this, and one who misses Friday prays Dhuhr instead.
Hence, given our current situation, there is no problem in advising families to observe all of the Sunnahs of Eid (of taking a ghusl, eating a breakfast, wearing one’s best [permissible] garments, saying the general takbīrat after Fajr, etc.) and then praying a congregational prayer at home with one’s family.
The Eid prayer has special takbīrat. There are 7 takbīrat in the first rak’at inclusive of takbīrat al-iḥrām, and 6 in the second rak’at inclusive of the takbīrat al-qiyām – this is the position of the Ḥanbalī school, and Ibn Taymiyyah. Note that Shafi’is say 7 not including the takbrat al-ihrām (that would make 8 total); as well the Ḥanafis state 4 takbīrat inclusive of iḥram and qiyām for both rak’ats.
As well, the Eid khutbah is not a requirement of the prayer, hence there is no need to give one. All four schools of law state that the khuṭbah of Eid is not obligatory. In the report above, Anas (r ) merely prayed two rak’ats and didn’t ask his servant to deliver a khuṭbah. Alternatively, it would be allowed for masjids to broadcast Eid khuṭbahs, and all families pray their individual congregational prayers at a given time, and then, after they finish their own Eid prayers, they can listen to a khutbah broadcast live from their masjid as a general reminder.
And Allah knows best.