Backson,
Yes, you can indeed copy your settings from one user to the other. It takes a bit of experience to decide what should be migrated and what you should just take the time to set up again, but it can be done in a selective manner. Do be careful and only migrate what you really need.
The answer to your question is yes, Applications "should" keep all of your settings in a specific place, and most do a reasonable job of this. The correct place for user settings storage is within the "~/Library" directory for each user account. Every user on a Mac has a Library directory at "/Users/<username>/Library". It is the equivalent to the "/Users/<username>/AppData" directory on a WIndows 7/8 PC. Note that the Library directory is hidden by default. To browse to it in Finder, pull down the "Go" menu and then hold the "Option" key and it will appear on the drop-down menu. You can also use "Go" > "Go to folder" > type "~Library" > click the "Go" button. If you poke around in your Library you will see that it's not as simple as copying everything over to the other account. You should be selective and do some research about what to copy.
For example, you will likely want to migrate things like:
~/Library/Mail/
~/Library/Mail Downloads/
~/Library/Messages/
~/Library/iTunes/
~/Library/Calendars/
~/Library/Favorites/
~/Library/Keychains/<specific keychain files> (do some research about moving any keychain files)
~/Safari/
~/StickiesDatabase
~/Library/Preferences/*.plist <these are application settings files>
~/Library/Application Support/ <there are many application specific folders here that can be copied over>
Once you decide what things you want to migrate, copy them to a USB Flash drive that is formatted as Fat32 (as most are). You can then log into the other user account, and have access to the USB Flash drive to copy the items to your new account's Library folder.
Before actually migrating settings to the new user account make sure that you have a good backup of your new user account's Library folder!!! Then, you can go ahead and replace the existing folders, with the copies from your old account. Because you are copying from a Fat32 formatted flash drive, the old permissions will not have come along for the ride and the permissions will end up just as they should be (because your new account is writing the folders/files). Just make sure to copy the folders/files to exactly the same place that they were on your old account (this will require replacing existing directories).
One important thing is if you copy a directory like ~/Library/iTunes, you need to also make sure to get any obvoiusly related directories from ~/Library/Application Support/, and from ~/Library/Preferences/*iTunes*.plist. These things go together and often times the settings are contained in a .plist file yet your actual user data is contained in the other directories.
Once you are done, you should be able to launch the applications that you moved preferences for and they should have your settings as you left them in the other account.
When in doubt, just Google something like "Mac OS migrate <application name> to new computer" and you will find the paths of the directories that you need to migrate.
Lastly, to reemphasize, make sure that you have a full backup of your account(s) prior to trying this. And, make sure to not get over ambitious with what you migrate. Only take what you know you need and leave the rest of the baggage behind.
Good luck.
