No one is born a sinner and the newly born is innocent until they can distinguish between right and wrong. They are accountable for all there actions after Puberty and if they are mentally able to do so therefore the insane are not held accountable.

As for the Prophets(AS) they were all Innocent but capable of making mistakes, they were all trialled and none is perfect.

All the Prophets(AS) was perfect in their delivery of the message, but they were Human and capable of making mistakes and their trials are the hardest:
Abu Saeed said: “Messenger of Allah, you have a very high fever”. He said: “We are like this: our trials are very hard and our reward is multiplied.” Abu Saeed asked: “Messenger of Allah, which people have the greatest affliction?” He replied: “The Prophets (Pbuh), and then the most pious and righteous. Any one of them may be tested with poverty until he could find nothing more than a robe to cover himself with and he would wear that. Another could be tested with fleas until they almost killed him. They were more pleased with their affliction than any of you may be pleased with gifts.” (Related by Al-Bukhari in Al-Adab Al Mufrad).

However whenever A prophet did make mistake, they were quick to repent:

"Allah accepts the repentance of those who do evil in ignorance and repent soon afterwards. To them will Allah turn in mercy. Allah is full of knowledge and wisdom"
Sura 4:17

Therefore the Prophet are not perfect human beings, however they were the best amongst the people they were with and perfect for delivering the message and chosen by Allah(SWT):

Adam's progeny declared: "Our Lord, we bear witness that You are our Lord; we have no otherLord but Allah. Allah raised their father Adam, and he looked at them and saw those of them who
were rich and those who were poor, and those who had good forms and those who did not. Adam said: "O Allah! I wish You to make Your servants equal." Allah replied "I love being thanked."Adam saw among the prophets like lamps among his progeny.