Re: preventing re-registering of secure sites upon opening website
While it could vary from site to site, the most likely method of saving that data is a cookie. Other possibilities include information saved in local storage (DOM storage) or a Flash LSO (sometimes called a Flash cookie or supercookie).
Even when the site finds the locally saved data, it may require your username and password, but it usually would not persist with the additional questions.
Some sites may also link your cookies to your IP address. Usually your IP address is stable in any given location, but if you use a private VPN service or TOR to anonymize your connection, it may vary.