For example, a woman converted at the age of 25, would she be able to show her pictures which were taken before she converted (age of 24 for example) and with her hair showing?
This is roughly IMPERMISSIBLE, since it is found in the Quran that The hair of a woman shouldn't be shown since she is Mukallaf, and the hair in that picture is therefor 'haram to be seen.
There is no direct proof in the Quran than a woman must not show her her before she is Mukallaf. That is from your Marje', according to Sayed Ali al Khamenai, this is not permissible.
From the Quran about woman wearing Hijab
وَ لاَ يُبْدِيْنَ زِيْنَتَهُنَّ إِلاَّ مَا ظَهَرَ مِنْهَا وَ لْيَضْرِبْنَ بِخُمُرِهِنَّ عَلىَ جُيُوْبِهِنَّ
“...and not display their beauty except what is apparent, and they should place their khumur over their bosoms...”
يَا أَيُّهَا النَّبِيُّ, قُلْ لأَزْوَاجِكَ وَ بَنَاتِكَ وَ نِسآءِ الْمُؤْمِنِيْنَ: يُدْنِيْنَ عَلَيْهِنَّ مِنْ جَلاَبِيْبِهِنَّ...
“O Prophet! Say to your wives, your daughters, and the women of the believers that: they should let down upon themselves their jalabib.”
Mukallaf: The person whose sins are being registered and the obliged duties must be done. Even more verses about Hijab: https://www.al-islam.org/hijab-muslim-womens-dress-islamic-or-cultural-sayyid-muhammad-rizvi/quran-and-hijab
Every woman in the world can show whatever she can. Your asking is very weird: why would somebody even tried to stop the woman from showing her hairs? We are not savages, we take care about our woman, about theirs rights to express themselves. I even think that woman are superior to man: they can give birth...