About Six Sahadats ..
One or Two witness needed to establish the sighting
The ulema agree that two trustworthy witness are sufficient to establish a crescent sighting
Abdur-rahman bin zayd bin Al-Khattab said that a number of Sahaba reported that the Messenger said “Fast when you can see it, break your fast when you can see it and keep the day count for sighting. If it is obscure to you then complete thirty days and if just two Muslims witnesses testify that they saw it then fast or break your fast.
(Musnad Ahmad, Sunan Nasai, Sunan Daraqutni, Imam Albani declares this Sahih hadith)
Then about the 2 year old child So i just said that when YR so called NA AHAL COmmette see the moon it is as big as and visble that even 1 two year old child can see it clearly.
About Scientefic methods So Prophet (S.A.W.W) ignored those things.Check the link which i provided in previous post.