Are women allowed to go to school? If yes, are their any restrictions they have to observe? I understand they may have to go to school alone at times (if not all the time), they might have to travel in public transport just to get to the school. Is this OK/acceptable according to Islam?
No, Quran does not forbid women from going to school. There is only a verse in Quran (relevant to the matter) ordering to only wives of prophet that they should remain in their homes:
And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. And establish prayer and give zakah and obey Allah and His Messenger. Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [extensive] purification.
وَقَرْنَ فِي بُيُوتِكُنَّ وَلَا تَبَرَّجْنَ تَبَرُّجَ الْجَاهِلِيَّةِ الْأُولَى وَأَقِمْنَ الصَّلَاةَ وَآتِينَ الزَّكَاةَ وَأَطِعْنَ اللَّـهَ وَرَسُولَهُ إِنَّمَا يُرِيدُ اللَّـهُ لِيُذْهِبَ عَنكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا http://tanzil.net/#33:33
But this command of God is only to wives of prophet; although one of them did not obey this and left her house and leaded a war. this verse does not apply to all women and every situation, most of verses only apply to a specific time and situation with the potential of generalizing.
There are some verses about hijab and affairs of women but they are different topics.
But if you consider only this topic, then there is no such verses in Quran.
Does Quran/Islam forbid women from going to school?
There is nothing in the holy scriptures of Islam that prohibits women from going to school. In fact, there is no mention of schools in the Islamic scriptures. School is a modern institution that didn't exist during the time of the Prophet.
Are women allowed to go to school?
Yes, it is permissible for women to go to school. But they should dress according to the principles of Islam.
If yes, are their any restrictions they have to observe?
There is a difference of opinion regarding this. Some scholar are of the view that men and women should be segregated. Some others disagree with this and permit co-Ed education.
My personal view is that co-Ed education is permissible because during the time of the Prophet, men and women prayed in the same mosque. Also, during the Islamic golden age, men and women studied and attended lectures together at the same place. My own views are not Islamic rulings but they are supported by narrations/hadiths and views of many Islamic scholars.
I understand they may have to go to school alone at times (if not all the time), they might have to travel in public transport just to get to the school. Is this OK/acceptable according to Islam?
Generally, most students attend schools that are very close to their homes (within 5km). If this is the case then it's permissible for them to go to school alone. According to the majority view, if the school is more than 48 km away, then it is not permissible for a women to go to school alone. But some modern scholars disagree with that and consider women going to school alone as permissible regardless of the distance.
With regard to "travel in public transport", if they preserve their modesty while travelling by public transport then there is nothing wrong with that.
Like boys , girls may be sent to schools and colleges for acquiring knowledge . If a girl is educated she can uplift a family and finally a small step to improve the society.She will be a support to her husband and family by all means.May Almighty bless all the Muslim girls to acquire knowledge and lead a happy and meaningful life.