Let's go through the points you've addressed.
First of all as you said in Islam there's no fix prescription for a marriage age. However such marriages in general could be regarded more like an exception than being the usual case -today even more than in earlier times-.
These prescriptions rather are based on social perception of the matter. Maybe 1400 years ago marrying at 9 years was rather acceptable and still is in some regions of the world. Elsewhere society expects girls to study, to have completed their school education before getting married etc.. Therefore in many countries - even Muslim countries - a minimum marriage age has been established and even enforced by law.
Secondly scholars agreed upon the fact that in case of such an early marriage parents (mostly fathers are named) would chose when the girl is "ready" for marriage until then she shall stay at her parents home.
In my answer on Are women who are divorced after the consummation entitled to maintenance? I've addresse the meaning of the verses 65:1-7, what does this mean?:
If the wife has moved to her husbands home before talaq was uttered, she shall and must stay there. But if she is still living at her parents home she wouldn't be obliged to move to her husbands home as she shall stay in the house in which she usually stays -even if it would have been a duty of her husband to house her after marriage-. In any case her maintenance would be a due for her husband until the 'iddah -if any- ends.
Sinn az-Zawaj سن الزواج
Actually means marriage age unlike what you've claimed.
Talaq and the corresponding rulings on the wife based on the "status of the marriage"
In fact woman who have been divorced (by talaq) are one of four kinds:
- a woman who has been divorced after both consummation of marriage and specification of mahr (sadaq) this was covered in (2:228).
- a woman who has been divorced before both consummation of marriage and specification of mahr which is covered in the verse displayed and explained below (2:236). Where a gift of value is regarded as a compensation instead of payment of mahr.
- a woman who has been divorced before consummation of marriage, but after specification of a mahr which is covered in (2:237).
- a woman who has been divorced after consummation of marriage, but before specification of a mahr which is covered in (4:24) and the reason why scholars say: mahr is not a condition for marriage being valid, but consummation of marriage makes mahr a due on the husband.
See also Tafsir al-Qurtobi page 612 here.
Further Allah the almighty says:
There is no blame upon you if you divorce women you have not touched nor specified for them an obligation. But give them [a gift of] compensation - the wealthy according to his capability and the poor according to his capability - a provision according to what is acceptable, a duty upon the doers of good. (2:236)
So if talaq was uttered before spouses (could) have been intimate nor a mahr (sadaq) was agreed upon. The husband is asked by Allah at least to leave a gift of a value based on his wealth as a compensation. This is agreed upon by all scholars according al-Wahidy الواحدي in his tafsir (see also in this article -in Arabic-). Al-Qurtobi however said that most scholars considered it a due understanding this as an order while others among them imam Malik consider it a recommendation due to the wording "a duty upon the doers of good". Al-Qurtobi also mentioned a third view saying that half of the -commonly practiced- mahr is a due on him which is against the a majority view of giving a gift.
Privacy or intimacy is mainly regarded as equal to marriage consummation
Finally in case that both husband and wife have been together alone, without company from a fiqh perspective (majority view) consummation of marriage was possible and therefore both talaq and 'iddah are necessary to dissolve the marriage.
You may read for example in al-Mawsu'a al-Fiqhiyya الموسوعة الفقهية الكويتية:
here and in the following I'll be translating from Arabic as these translations are based on my own efforts take them carefully!
6 - تجب العدة على المرأة بالفرقة بين الزوجين بعد الدخول بسبب الطلاق أو الموت أو الفسخ أو اللعان ، كما تجب بالموت قبل الدخول وبعد عقد النكاح الصحيح . وأما الخلوة فقد اختلف الفقهاء في وجوب العدة بها :
6 - The waiting period for the woman is required by the separation between the spouses after consummation of marriage due to divorce, death, annulment (Faskh) or curse (Li'aan), as it is required by death before consummation and after the right marriage contract.
As for being alone (Khulwa), the jurists differed as to the necessity of waiting for it:
فذهب الحنفية والمالكية والحنابلة إلى أنه تجب العدة على المطلقة بالخلوة الصحيحة في النكاح الصحيح دون الفاسد ، فلا تجب في الفاسد إلا بالدخول ، وذهب الشافعية إلى أن العدة لا تجب بالخلوة المجردة عن الوطء .
The Hanafis, Malikis and Hanbalis are of the view that the waiting period is required for the divorced woman by proper seclusion (Khulwah sahihah) in a correct marriage without the corrupt, so it is not obligatory for the corrupt except by consummation. While Shafi’is said that the waiting period is not required through private seclusion from intercourse.
See also fatwa islamweb #129370 in Arabic.
The majority view is based on reports showing that the rashidi Califs and some Sahabah acted upon or ordered this, see for example in Mosannaf ibn abi Shaybah
مصنف ابن أبي شيبة:
حدثنا جرير عن منصور عن إبراهيم قال : قال عمر : إذا أغلقوا بابا وأرخوا سترا أو كشفوا خمارا فقد وجب الصداق .
Jarir told us on the authority of Mansour on the authority of Ibrahim who said: Umar said: If they close a door and release a veil or uncover a veil, the dowry is required.
See also in al-Muwatta' here and here and similar records in Musnad Ahmad, Sunan Sa'id ibn Mansur, Mosannaf 'Abdurrazaq, imam a-Shafi'i's al-Umm and elsewhere. The statement means that 'Umar -as is the case for the displayed report- considered the marriage has been established.
The later view of imam a Shafi'i however is based on the apparent meaning of verse (33:49).
In any other case what applies is (2:236) -if mahr was not yet specified- or (2:237) -if mahr was specified-. As for the related waiting period ('iddah) Allah made it clear in:
O You who have believed, when you marry believing women and then divorce them before you have touched them, then there is not for you any waiting period to count concerning them. So provide for them and give them a gracious release. (33:49)
So 'iddah doesn't apply if intimacy or more exactly marriage consummation didn't happen.