If I obscure my IP by going through a free http proxy and visit a page, will that site's admin ever be able to find out my true IP or anything related to my true connection/info?
Just because your traffic is passing though a proxy it doesn't mean you are safe. "Transparent" proxies will transmit your IP address using the X-Forwarded-For HTTP header. There are also cookies that can be used to identify you, such as flash's evercookie. You can even be fingerprinted and tracked by the extensions you have installed and what versions you are running using The EFF's panopticlick.
Using Tor in Firefox from an open wireless access point works well. Ironically, the fingerprints gathered by EFF's panopticlick is used to make the Firefox's anonymous mode more difficult to track. This is because Mozilla and the EFF are working together on this project.
This is a huge question with amazingly huge overhead. But at the same time, it can be whittled down to a simple answer: no.
My first questions are about the network design. Are you looking to hide your private network IP address or your public facing IP? Is the proxy part of your infrastructure? Are there other network devices at play (i.e. NAT enabled devices). If you are looking to obscure your private address, that is a much more obtainable goal. Also in that case, the proxy isn't the necessary step (though it may give the same functionality), Network Address Translation (NAT) would be the key. And you still would would need to lock down your firewalls, browser, etc.
The other responses covered the other part of the picture. With how dynamic web sites and web services are today, there are many means other than just your source IP address that a potential attacker or investigator may leverage to find out your information.
Please include the reasoning behind this question. If you are doing this simply for securing your identity, then this is one of many steps you will need to take. If you are thinking about doing something malicious, please reconsider and if nothing else realize that needing to ask such a generalized question should tell you that you would inevitably be found out (no offense).