No, the visitor must click on your Adshrink.it link because they wish to go to the destination website. You may not offer any incentives to your visitors to click on your Adshrink.it links.
You may click on your own links once to test them but you are not credited for those views. You cannot click on your own links to generate money.
Everyone can register an account, however if you are using the same computer or the same internet connection, you cannot be referred by each other.