Quite a few questions here. But as for your first question on the great sacrifice of Jesus (as) which you consider to be for all of humanity, as opposed to Allah merely forgiving everyone without any loss, it is merely two different perspectives. The Islamic view is that Allah is so Transcendent, then why would He ever have to stoop so low as to become a human being that is born from a woman, grow up and then simply die? Allah is considered so beyond that, that He does not need to do this.
The arguments for why the Muslim and Christian perspective differ are easily understood when they are outlined point by point:
#1 God is One: In Christianity, God is Three and One. Therefore, the two other parts help to make the whole. In Islam, God has no other part to Him, it is just Him. Therefore, is only Him Who forgives and only He is worthy of forgiving.
#2 No one bears anyone else's burden: In Christianity, the belief is different and Jesus (as) is considered to have borne all of humanity's sins. Although, in reality, this is just that section of humanity that accepted him. In Islam, those who accept Allah as One without any partner, are liable to be forgiven because they realize that it is only Allah Who created them, and no one else. Jesus (as) is a Prophet of Allah, and not the Word of God that existed with Him since eternity.
#3 All praise belongs to Allah: This is so vitally important that it is the basis for all of the actions of a Muslim. It is in the first Surah of the Qur'an, and so it is part of the "Mother of the Book" (Mother of the Qur'an). This means this verse encompasses a lot of meanings, undisputably so. Jesus (as), having been born of a mother, being liable to birth and death, hunger and sickness, etc. He is not worthy of being considered "God". He did not create the universe with Allah, and thus he has no right over His creation. Indeed, since Christians believe that Jesus (as) was only the Word and then became personified 2000 years ago, both sides agree Jesus (as) was not present in creating the universe. No "Word" of God created the universe. It was One God in the Bible which created the universe. Thus, all praise belongs only to Allah, Who is the Lord of all the Worlds - He is worthy of all praise, because He created the universe. This now included the second verse in the first Surah of the Qur'an. It presents an argument throughout the Book, which is that Allah is worthy of all praise, and no idol, human, jinn or angel, etc is allowed to be worshipped or considered worthy of forgiving and punishing, except Him.
#4 Question: If Jesus (as) is worthy of forgiving, then is he worthy of punishing? For the one who forgives, has to punish as well. Otherwise, how can Hell exist?
These are just four points to ponder upon. These should be some food for thought as to the differences in why us Muslims believe in only Allah as the Transcendent Being Who can forgive, and why we do not consider Jesus (as) to be worthy of forgiving mankind.
Forgiveness in Islam is about sincerely repenting from your heart for the wrongs you have done, not washing it all away, literally, by being bathed in a river and accepting Jesus as the savior who forgives us. Allah forgives a servant for his wrongs when he asks Him for forgiveness. For us Muslims, Allah is so Powerful and Transcendent, that He has no trouble forgiving anyone. This means, He does not require a sacrifice. It is easier than that for Muslims. The Christian attitude is that out of sympathy for the suffering of Jesus (as), you accept him and then you are forgiven because you feel he died for you. Because of this empathy, you accept him. It creates this emotional swelling to accept him since he gave up everything for you. Yes, it is emotional alright. However, the facts must remain as facts. All I see are a sea of emotions swelling when I see how Christians accept Jesus as their savior who died for their sins.
As for babies being born pure and as Muslims in Islam, who have not sinned, compared to the Christian view, you wonder when do children start to sin in Islam and why?
When kids reach puberty, which is considered to happen in many different ways in Islam. At the age of 10, children who ignore prayers are allowed to be hit by parents so that they can see the harm in rejecting prayers. This is in fact the only situation where the parents are allowed to hit children in Islam
As for what constitutes sin in Islam, it is simply the disobedience to Allah. In other words, whatever we feel what we are doing is wrong. We humans are born upon the natural tendency to lean towards Allah, so when we reject Allah's message, we reject that part of our natural self which is meant to be at peace with Allah. Otherwise, we know no peace when we reject Him. Thus, evil is the rejected of Allah and disobedience to Him. We ask for forgiveness of our disobedience to Him because we ourselves commit these crimes, no one else.
Salvation requires steadfast obedience to Allah, and it requires a great effort on our part. Salvation is not by accepting a savior for Muslims.