Gmail – How to delete all archived emails

The default is to delete the entire conversation. If you're hitting the big "Delete" button near the top of the page then that's what is happening.

However, it is possible to delete individual messages from a conversation. While viewing the conversation you need to open the menu for the individual message. (It's the down arrow next to the reply button.) From there you can delete an individual message from a conversation.

As you mention, that's going to be labor-intensive. You're probably better off turning off conversation view altogether if you're going to be doing this regularly (as mhoran suggests).

The only way to lose a message is to delete it. Archiving a message will never delete it.

Assuming that a filter isn't used to automatically apply a label, the incoming email will only have the inbox label. As you work with the message you can manually add multiple labels.

The Archive command removes the inbox label from the message/conversation. If the user never added additional labels the only place to find it is in all mail. If the message/conversation had another label added to it, that label remains.

To find the email with a label you can use the sidebar listing of your labels, or use the search tool including the string "label:labelname" (don't include the quotes).