First you should read the online documentation (specifically the 'Manual' page). If you have further questions, you may post questions to the Users Forum.
Yes. WebInject uses the SSL/TLS library from the OpenSSL toolkit. Secure Sockets Layer (SSL v2/v3) and Transport Layer Security (TLS v1) protocols are supported.
Yes. HTTP Basic Authentication is supported.
Yes. WebInject automatically handles HTTP Cookies for you. When a "Set-Cookie" is sent back in the HTTP header from the web server, the Cookie is stored and sent back with subsequent requests to the domain it was set from.
Yes. Cookieless session handling and state management is possible by parsing data from an HTTP response and storing it to be resent in subsequent requests. See the Manual section on "Session Handling and State Management" for information.
Yes. See the section in the manual page on Configuration. There is a setting you can add to config.xml to specify a proxy.
No. I opted not to implement redirects from the WebInject engine. If the server responds with an HTTP redirect response (301, 302, 307, etc.), you must add another case to request the URL you are being redirected to. There will always be a single response for each request.
No. WebInject works at the HTTP protocol level. It is not a GUI driver or browser automation tool.
This error is coming from your Perl interpreter and it is letting you know that your Perl kit is missing some modules that WebInject requires. You must install these modules on your own. See the Build Page for more information on Perl modules.