There are a few prisons that allow certain inmates to have access to computers the internet for education purposes but most prisoners are not allowed computers or any access to the internet for security reasons.
However some prisons allow video visits from the prison to the visitors home instead of showing up at the prison they can have a conversation over the internet but it's very secured.
The questions about Prisoners on Quora are actually answered by prisoners but the answers are typed out by volunteers who have access to the internet at their office or somewhere else.
So while it may seem like the prisoners are talking to people on Quora it's really someone else typing it out.