If I'm using iMail with a Gmail account when I delete messages in iMail will it carry over to Gmail?

It does that for me. I use Mail with Gmail, and when I delete an email in the Mail App, it's not there when I sign in on Google.

Gmail is normally set as an IMAP account, which means that the emails are not stored locally on your computer, like they are with a POP account. Examples of POP accounts are like a time warner email, a cell phone carrier email, such as ATT.com, etc. What this means in regards to your question is that yes, when you delete an email from your gmail account on your mail application, then it will be deleted on your phone and other devices as well. An IMAP account works like iCloud - any changes are saved across your devices that gmail is logged into.

However, you can create a mailbox in your mail application and select it to be "On My Mac" then move any emails that you want physical copies of into it. That way, they are on your Mac until you delete them and not stored in Gmail. These emails in the "On my Mac" folder are backed up when Time Machine backs up your data if you have that running.

Then how do you empty your archives? Thanks for the instructions, they were helpful to me as well.

If you have an archive in your Gmail account, and it has added properly to your iMail application, then you should see a blue folder listed under your mailboxes (same area as your inboxes, sent, trash, etc) and it is titled Archive. If you don't see this folder then there is nothing in your archive. To add something to your archive, simply select a message, and hit cmmd+opt+A in order to move it to your archive, and then once a message in there, it will show on the left in the list of mailboxes.

To delete messages in your archive, you do it the same way that you would delete your trash or your main inbox. Simply click on the first message, and select all (cmmd+A) and then they will all be highlighted. Click the trashcan on your toolbar within mail to delete it and they will be deleted across all your devices and from the Gmail server - so ensure this is what you want to do.