A: An insecure network is an insecure network – regardless of the physical or geographical location.
As to how unsafe it may be, depends on your definition.
The biggest issue is the good possibility that your network traffic is watched. This means that any username, password, or other sensitive information you enter may be viewable by some creep in or near the library.
If you are using your own computer,
If you are using the library’s computer, you won’t be able to install software, so VPN and tor are not available to you. The only alternative is to ensure that whenever you may need to enter sensitive information, the webpage is encrypted. This displays differently in different browsers, but you may either have a lock icon in the address field, or the URL will start with https, instead of http.