#2 - Yes, this is new with v11+. In v10 and earlier the client was registered automatically when you logged in to QC. That is why you had to have admin rights to run v10 and earlier.
#1 - There might be a way for you to bundle the client DLL with your application, but then your end users would need admin rights to install you application so that the DLL could also be registered. I'm not an expert on creating installable applications so I can't offer any tips on that.
I can think of two ways to avoid having each user register the client. One is to change your application to be a web application, install it on a web server where the client is registered, have your end users access the web page, and have all the execution run server-side. Another way is to put the application on one machine and have your users all access that one machine to run the application.
#1 - There might be a way for you to bundle the client DLL with your application, but then your end users would need admin rights to install you application so that the DLL could also be registered. I'm not an expert on creating installable applications so I can't offer any tips on that.
I can think of two ways to avoid having each user register the client. One is to change your application to be a web application, install it on a web server where the client is registered, have your end users access the web page, and have all the execution run server-side. Another way is to put the application on one machine and have your users all access that one machine to run the application.