Some time ago I configured my Gmail web site account to be linked to my OS X Mail 4.5. So I get all of my Gmail and send all of my Gmail from my Mac 4.5 client.
When one configures the Mac 4.5 to add the Gmail IMAP account various folders are created by default on the 4.5.
In addition one can add their own folders.
Question: If I go to the web based Gmail and delete all the mail what about the mail I sent or received via my Mac 4.5. Will those copies that are deleted on the web site be deleted from the folders on my Mac 4.5, either my customized folders or the ones added by Gmail?
If you set it up as an IMAP account then the Mail.app just reflects what's on the server. So if you delete them from the server they will also disappear from your computer. If you just want them on the computer create a local Mailbox. Mailbox -> New Mailbox, make sure you create it under 'On My Mac.' Then move the messages to that folder(s). Then you can delete them from the server. FYI, gmail by default doesn't actually delete anything, instead it moves it to your 'All Mail' folder.