Is it possible to set up KP so that when I create a new account online, KP will automatically create a new entry for me and save the password?
No, KeePass does not interact with your computer except to type characters.
You can use a plug-in that may allow you to do this - see Integration and Transfer on the plug-ins page.
What do you think about security of these addons? Did they test anyone?
I saw it: The plugins offered on this page are developed by different, independent authors. The KeePass team cannot check all plugins for bugs and malicious code before they are distributed here.