Can you bring your own laptop in your city library and work on it?
Of course, only you probably will not have free access to the Internet there.
Of course you can. I like to study and work in the city library rather than at home because there's less distraction in the library for me.
Some libraries have extra workspaces with group tables, single tables or even workbenches. In addition, some libraries even provide Wi-Fi. Just ask.
Why do not you ask such a thing in the library itself? Maybe they have their own rule about something like that?