Re: Muhammad (SAW) and his wives
Quran 4:6 … Test the orphans when they reach the age of marriage (Balaghu-un-Nikah). Then if you discern in them maturity, deliver to them their property. And do not consume it lavishly and hastily lest they should grow up. As for him who is well-off, let him be abstemious, and as for him who is poor, let him eat in an honourable manner. And when you deliver to them their property, take witnesses over them, and Allah suffices as reckoner.
[Even though, 'Surah Nisa' was revealed around 4H, we should know that for Prophet (SAW), it is our belief that he (SAW) never did anything in life that was against Islam ... hence, even though Prophet (SAW) married Aisha (RA) before this ayah, what is mentioned in this ayah applies on Prophet (SAW) life too ... and a Muslim should not even think that Prophet (SAW) would have done something in his life that was against Islam].
Thus, from above ayah, it is clear that there is age of marriage (Balaghu-un-Nikah) in Islam. Above ayah also tells when that age happens, as according to above ayah, that age is also age of maturity, not just physical maturity but intellectual and economical maturity too … or awareness of economical interest. It is because, at this age, person who is holding assets of an orphan should test them (orphan) and then handover those assets to the orphan (this is recommended because, some children never grow or become money conscious even when they are grown up, and thus, for their own good, their assets should be managed even when they are grown-up).
Knowing or being aware of economical interest is necessary for a person getting married, because in Islam, marriage starts with money transaction … Money related to Mahr is given by groom and received by bride … and to do such transaction, both (bride and groom) should be aware of their interest (especially, economical interest and its value to their life).
Similarly, Islam wants both boy and girl getting married consent to marriage themselves in front of wakil (nikah-khwa) and witnesses. No one can take that decision on their behalf. That decision making also needs a certain age where both boys and girls are mature enough that they could take such decision on their own. Only an ignorant would believe or say that such important decision of life (accepting of life partner) can be taken by an immature under 15 years old.
Above two factors, that is taking decision of making life partner by bride and groom, and exchange of money, is not there in any other religion except Islam' (as far as I know, no religion gives such responsibility on both bride and groom as religious requirement in marriage)... hence, for such to happen, certain age of maturity becomes essential requirement.
Islam is religion where when laws are made or given by Allah, it is for average cases (or persons) and not for exceptional cases (or persons) ... so, if there are any exceptional cases than they have to follow the law that is made for average persons, especially, when an exceptional case person can follow the law that is meant for average case persons.
So, above ayah is clear that marriageable age is average age when boys and girls could look after their assets properly (take responsibility of their wealth and financial possessions). It is obvious that average 10 or 15 years old boys and girls could not look after their economical interests or manage their assets. It is safe to say that this age of economical awareness is somewhere above 15 or 16 years of age (widely accepted age for such purpose), and thus that is the minimum age of marriage (according to Islam). Similarly, life awareness should also be there in both boy and girl, that they can choose right partner for themselves on their own responsibility, that no one can expect from under 15 years old.
It means, whoever marries 9 or 10 years old, they are disobeying Quran, what obviously Prophet (SAW) or any pious Muslim of his time could not have done.
That is different matter that later Muslims brought culture of their own religion when they became Muslim, and thus young boys and girls start getting married in Islam too (against clear ayah in Quran, that marriageable age is age when a child becomes economical aware and money conscious).
As for Aisha (RA), according to all known historical sources, she (RA) was 10 years younger than her elder sister Asma (RA). It is also known from all known historical sources that Asma (RA) was 100 years old when she died in 73 Hijri. That means, Asma (RA) was 27 years old at the time of Hijrat and it means Aisha (RA) was 17 years old at time of Hijrat.
Thus, following historical sources, Nikah of Aisha (RA) happened around 2 years before hijrat (when she was around 15 or 16) and rukhsati (marriage) happened a year or two after hijrat (around 3 years after Nikah) when she was around 18 or 19.
Note: Khadija (RA) died 10 years after prophet-hood, or 3 years before Hijra ... when Prophet (SAW) was 50. Prophet (SAW) married Sauda (RA) few months after the death of Khadija (RA) … and then Prophet (SAW) married (brought into nikah) Aisha (RA) a year or two later.