For IIS 7, do you know where to configure number of connections from application pool

It should be as easy as creating a new web that points to the folder where /mysite is, then modifying the properties so that it accepts requests with the host header mysite.mydomain.com.

Here's a technet article on setting the host header:

Type appcmd list apppool, and use exactly what it lists there in your appcmd start apppool /apppool.name:

Names with spaces should be escaped with double quotes. For example:

%SYSTEMROOT%\System32\inetsrv\appcmd stop apppool /apppool.name:"My App Services"

Post the exact command you're trying to run ; perhaps you missed the colon or there's another problem with the syntax?

Edit - you're adding a space between the colon and the first double-quote. Remove that space, use the double-quote, and see what happens.