Where does gdebi put the file after it is opened and where is it after gdebi extracts it, same question for .gz after it is unzipped where does the file go and same with transmission. also
After the .deb file is opened does it lose the .deb after the end of the file name and again same with .gz . After the torrent file is opened is it named the same without the .torrent at the end of it.
Is their a way to find these files after opening and extracting and unzipping with the use of a program. My terminal isn't finding the opened gdebi files or the unzipped .gz file

If I understand your question, I think that once the .deb package is installed (by gdebi, apt-get, aptitude, etc.) the original .deb file is deleted. Once a .gz is unzipped the original archive stays wherever you downloaded it. For example, if you downloaded it to ~/Downloads then that's where you'll find it.
From a terminal type this two commands:
jdk

Basically where files are stored depends on application used to open that file. The same applies to what happens with opened file. For example, KTorrent can delete .torrent file after adding it to queue. "gdebi" does not just extract files, it will install it, and as i known it will not delete orginal file. It depends on program included in .deb package where it will be installed. You can look inside with some uncompress tool and you see there directory structure, there is also an install script. The uncompressed content usually goes to current working directory, with or without directory structure included in archive - it depends on used options.

To get full answer you need to specify which program are you use for these tasks.