Generally, how much freedom of movement a general Roman woman would have? Did it differ between young and old? Were young girls allowed in the public spaces? Did they need a chaperone?
I understand I'm not referring to a specific time in my question, because I'd be interested to hear in general or specifically by different periods.
Edith Hamilton's "The Roman Way" would certainly answer some of your questions.
In general female Roman citizens, especially these of the Patrician class, had considerable freedom in many ways compared to say, Greek women. However, they were quite restricted compared to modern standards. Roman women citizens of significant class might be married at their teens or 20s and it was common for them to be educated at least to elementary school level (reading/writing, etc.)
Since men could be away for long times due to battle, and a noble family might own multiple homes, they were busy managing household affairs on their own for long stretches of time, including commerce, producing fabric (spinning wool), husband's business, and entertaining official guests at home. They could own property and do business even if they couldn't enter politics and a good Roman matron was considered to be smart with money. Many high class women ran shipping businesses in the days of the Empire.
Vestal Virgins had an interesting lifestyle and yes, they were out in public for ceremonies, but they could face death for breaking the rules.
This article covers rape under Roman law and discusses cultural context for such. https://repository.law.umich.edu/cgi/viewcontent.cgi?article=1084&context=mjgl
Women could initiate divorce, and they could be emancipated from paternal or husbandly authority and conduct their own affairs alone. They also could conduct their legal affairs- own lands, write wills, and appear in court. Remarriage was common in the elite and usually remarriages did not require paternal consent.
The paternal line guardianship of women diminished as the Roman empire evolved-- the first few Emperors dropped restrictions on women.
You might enjoy reading up about Fulvia, who commanded troops during the last civil war of the Republic. She had her face on coins. She had many marriages, including to Mark Anthony. Her daughter married the future Emperor Augustus.
One interesting bit about Rome itself is that ordinary people didn't have kitchens at home; they were fire hazards, so they basically ate takeout/street food all the time, and there was always a bustling business in food, drink, often run by women. Another factor in additional security were dogs. Ancient Romans loved dogs as pets, guards, sheepdogs, etc. and had them on leashes, and they had lapdogs too. Dogs would be guarding places of businesses. https://www.worldhistory.org/article/1603/dogs--their-collars-in-ancient-rome/