Allah is full of Mercy. Allah is Mercy in Absolute Term. No one who asks him for forgiveness, will He turn down. Absolutely, Allah is Mercy Perfect, and Mercy Absolute.
I have a question about Adam and Eve. Both were the first human created by Allah Almighty. Both were the closest to Allah, as they were the parents of the human beings communicating with Allah directly. Have you ever wondered when Adam and Eve committed such a small mistake/fault/offence...why did not Allah readily forgive them? If mercy is His greatest attribute it was the best time to demonstrate mercy and love as Adam and Eve repented many times. Yet Allah hid His face from them and expelled them out of Paradise. Would you expel your own children to the planet Mars for their first mistake? This shows that Allah is incapable of mercy. The concept of mercy is just a catchphrase by Prophet Mohammed to catch all into buying into his idea.
I do not think that your deduction totally rests on the above-mentioned incident. However, I will confine myself to the explanation of the true picture of Adam's falling into mistake and then his settlement in the earth.
The most important point regarding the narrations in the divine revelation especially the Holy Qur'ān is that it does not relate an event for the sake of amusement. It always has special purpose behind these narrations. The Qur'ānic narration regarding the incident of creation of Adam and Eve and subsequent events is no exception.
The basic purpose of the related verses occurring in Surah Baqarah can be pinpointed by looking into their proper context.The Surah (al-Baqarah) is addressed to the People of the Book and the verses dealing with creation of Adam and related issues are brought to depict the attitude Jews had adopted towards the Messenger of God Muhammad (saw). The Jews countered the new message bitterly because of their pride and envy. Some other groups hesitated in the beginning but once their doubts were cleared they accepted the faith. Qur'ān tells that this attitude is identical to the one adopted by the Satan and the angels. When Allah decided to create humans He told the angels His plan. They were not clear about the matter and expressed their concern. Their reservations were caused by their unawareness of the whole scheme. As soon as they came to know the scheme they accepted and praised God's wisdom and knowledge. On the contrary Satan opposed the scheme and refused to obey God only because of his pride and conceit. He thought that he is superior then why should man be made vicegerent of God on Earth. And why should he, who was made out of fire, bow before Adam who was made out of clay.
The role of the Jews was identical to that of Satan and of others who once their questions were sufficiently answered clung to the faith to that of the angels.
Adam and Eve were not ordered to spread in the earth as a punishment rather it was a part of the scheme the Almighty had for Adam and his progeny. The world Janna doesn't necessarily imply the paradise, which is the abode of the pious ones in the Hereafter. In fact the portrait the Qur'ān draws of that Janna tells that it is something to be created at some time in the future. It is obvious from the Qur'ānic description 'I have ordained to create a vicegerent on Earth' that it was decided from the beginning that the human were to be settled on the Earth. All the following events counted in the Divine Scripture show that these were meant to educate Adam.
The Holy Qur'ān does not state that Allah told Adam to descend on the Earth from a supposed Jannah. Rather they were told to leave the place they previously abode. The word'Ihbiṭuū" (إهبطوا) is commonly misconstrued. It does not necessarily imply to descend from a high place to a lower one. It also connotes to leave a place and to settle somewhere as in:
And when you said: O Moses! We are weary of one kind of food; so call upon your Lord for us that he bring forth for us of that which the earth grows of its herbs and its cucumbers and its corn and its lentils and its onions. He said: Would you exchange that which is higher for that which is lower? Settle into a town (in an Egypt to be more accurate as they wanted to use these things, which they were previously accustomed to eat. It is also an ironic statement which reminds them of their miserable lives in Egypt before exodus) thus you shall get that which you demand. And humiliation and wretchedness were stamped upon them and they were visited with wrath from Allah. That was because they disbelieved in Allah's revelations and slew the prophets wrongfully. That was for their disobedience and transgression. (2:61)
The order to leave the garden has been mentioned twice in the episode. In fact Adam committed a mistake and then adopted appropriate attitude and developed a sense of repentance. The humans are endowed with the conscience and this conscience rebukes them on a slightest of a mistake. That is why seeing that Adam has adopted right course of action God granted him and Eve with the words to seek forgiveness.
The order first is issued after their committing mistake as an admonition. Next time it uncovers the real scheme of God. Now the statement that Allah would send His messengers and they would endeavor to bring the humans to the righteousness follows it. And those obeying Allah's guidance will be blessed and the rejecters will be punished.