How do I check why my mailbox is taking so much space? How do I remove unwanted emails from it?

You can login to your mailbox (email account) via webmail at this address:
Username: email address
Password: the password of that email account

[ replace email address with your cpanel username if you need to check main mailbox ]

Once logged in, please select squirrelmail. Once in squirrelmail click on Folders to view all folders in your email account, and subscribe all of them, and then refresh folder list.

Now you can access all folders including spam box and check the emails in them.

If you have too many emails in a particular folder that you want to delete, here is one way to do that: There is a configuration option in squirrelmail from the top menu

Options : Display Preferences : Number of Messages per Page:

I usually set it to view 500 per page and go through junk emails quickly. Selecting all and deleting it. It will take a couple of minutes to delete thousands of emails. And you will be sure you are not stepping on system files.