Firstly: 

The difference among the Muslims with regard to determining the  first day of Ramadaan and the time for Eid al-Fitr stems from the differences of opinion among the fuqaha’ concerning the well known issue, which is whether sighting of the new moon in one country becomes binding for all other countries, or should each country have its own sighting. This also applies to determining the date for Eid al-Adha. 

This is a matter that is subject to ijtihaad, and each group of scholars has produced its evidence, and both groups may even quote the same text as evidence. This has already been discussed in the answer to question no. 1248. 

The view that sighting of the moon in one country becomes binding for all other countries is the view of the majority of scholars, and was the view favoured by Shaykh Ibn Baaz (may Allaah have mercy on him), as is stated in Majmoo’ al-Fataawa (15/77). 

The view that there may be differences in sighting between different countries is the more correct view according to the Shaafa’is, and was the view favoured by Shaykh al-Islam Ibn Taymiyah, and by Shaykh Ibn ‘Uthaymeen among contemporary scholars. We have quoted his fatwa in the answer to question no. 40720. 

Secondly: 

The differences among Muslims with regard to Eid al-Fitr and Eid al-Adha is based on this difference of scholarly opinion, and it is the same for both Eids. Shaykh Ibn Baaz (may Allaah have mercy on him) said, after mentioning the difference of opinion among the scholars about different moon sighting in different countries at the beginning and end of the month:                                            

It seems to me that the differences in moon sightings do not matter, and that what must be done is to follow the sighting of the moon with regard to starting and ending the fast and offering the sacrifice when it is proven according to sharee’ah that the moon has been sighted in any land. 

Then he said: Whether or not we say that differences in sighting are valid, it seems that the ruling is the same for both Ramadaan and Eid al-Adha, and there is no difference between them according to what I know of sharee’ah. End quote. 

Majmoo’ Fataawa Ibn Baaz (15/79). 

In the fatwa of Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) referred to above, it says that differences in moon sighting should be followed with regard to Eid al-Adha just as they are followed with regard to the beginning and end of Ramadaan. 

Based on this, there is no problem if Eid al-Adha is on Friday in one country and on Saturday in another, and so on, based on the differences in moon sighting. 

The same may be said with regard to the fast of Ramadaan, fasting the day of ‘Arafah and fasting ‘Ashoora’, because these are things that have to do with the sighting of the moon, and the ruling on whether the month has begun or not. 

And Allaah knows best.