1) No, the partner ID is not needed anymore.
2) We're looking in to it. I'll get back to you whenever I have the answer.
3) Which code would you like to post? All you need in order to integrate Socialize is to install the plug in.
4) If the buttons disappear then something must be wrong with your configuration.
For both the widget and main login configuration, you must enter the conf and login_params variables generated from the component designer. (you can use this page: http://www.gigya.com/site/partners/wfsocapi.aspx#&&userstate=LoginPageAPI) The following is an example of what you might put in the settings text area.
Note: Don't copy the entire code in the configuration page. Your code should look exactly like the example shown below.
UIConfig:'<config><body><captions background-color="#919148"></captions><texts color="#C876FF"></texts><background background-color="#FF6D6D" frame-color="#A4FFFF"></background></body></config>'