Hi, and welcome to the Apple (user-to-user) Community.
Re: "Mac Mail help please".
Apple support have articles online that may be helpful.
Wondering which MacOS version you have installed on your MacBook Air.
Eg: For accurate info.: if you are not using Mac OS 13 Ventura:
Please choose your MacOS version at the top of any articles that allow that change.
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Re: Why do I need an archive folder and why does it have so many emails?
In earlier MacOS versions, deleted eMails can reside in the Archive folder / mailbox / for a specified time.
or ... you can use that folder in any way you wish / eg: for keeping messages that do not belong anywhere else.
See: Archive emails in Mail on Mac - Apple Support for the most recent info.
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Re: "trying to clear out my inbox and remove large files"
Deleted eMails are dealt with according to how your settings are set up:
Eg: keep for 30 days in the Archive or Trash / Bin folder, (in case you want to retrieve email), or delete permanently.
Many of us find keeping deleted eMail very useful: "If you mistakenly delete messages, just drag them out of the Trash mailbox to another mailbox. Or select them in the Bin mailbox, then choose Message > Move to > [mailbox]".
The article below can help you to check / change / customise / your settings for deleted messages:
Delete emails in Mail on Mac - Apple Support
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Re: "I am unable to search for anything easily"
There are a few ways you can search:
How to: Search for emails in Mail on Mac - Apple Support gives some examples
and
You can also search for specific text in an email message: Find text in an email in Mail on Mac - Apple Support
More info: Filter emails / Sort emails / Flag emails / Show emails from VIP senders
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Re: "How can I make my mac mail more efficient? "
We all have our own ways of working efficiently. What suits one, may not suit another.
Eg: Ensure you see which incoming eMails are important, so you do not miss anything.
Sort and deal with incoming Mail as it arrives, day by day, keeping the Inbox free for incoming Mail.
Answer messages promptly, and file the eMail in a folder, if needed: have a "Backlog / Pending" folder.
Keep Mail in clearly-named folders, so it is easy to find anything and everything again, immediately.
Categorize messages:
You can have mailboxes (folders) within folders (Eg : "Holiday" can contain folders for several possibilities)
How to: Create or delete mailboxes or Rename mailboxes in Mail on Mac - Apple Support
How to choose settings to suit: Change settings in Mail on Mac - Apple Support
If you wish: How to: Use rules to manage emails you receive in Mail on Mac - Apple Support
Troubleshoot email problems in Mail on Mac - Apple Support
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Resource:
Mail User Guide online (or download a copy, eg: to the Books app):
Mail User Guide for Mac - Apple Support
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Support:
Mail Support Website: (info. / support / contact)
Mail — Official Apple Support
All the best :-)