I am getting auto-emails about the number of emails stored on the servers. There is a link provided in order to respond to the email, but this just takes me to help and support pages and I cannot find a contact email address. The online chat is not available as I have ad blocking on my browser. I have no idea I should need to remove browser security to respond to an email.
I have managed my emails in Outlook (this is the way I use my emails - not webmail) and removed all older and spam emails but still get the email messages. I have tried managing in webmail but this is near on impossible because of the way the mail is displayed (in pages not as a long list), making them difficult to sort and the problems with selecting more than one email - it seems you have to check each one individually, as holding the shift key to select a range doesn't work; if you accidently click in the wrong place it deselects the emails already checked so you have to start again.
Managing stuff in Outlook is by far the easiest approach ... but you do need to remember to empty the trash folder after "deleting" emails you want rid of.
Also take a look at your sent items folder. If like many people you use email to share photos, you could find that the send items folder is the largest. In Outlook (which version by the way) you can sort the items by size and look for the quick wins by getting rid of those having large attachments.
If you are using 'proper' Outlook (as shipped with Office) selecting "Show as conversations" on the View tab will group associated emails so that they can be deleted as a group. Similarly sort by title or sort by sender can be helpful in culling the inbox and sent folders.
As for Chat I would not look at it as "removing browser security" - blocking pop-ups can be very detrimental to a user's experience. There is nothing essentially wrong with pop-ups, it just that they can be annoying when abused. Also you can "whitelist" plus.net.
Webmail: CTRL/click and Shift/Click work as per-normal which in general can be a bit tedious. Under settings you can choose the number of items retrieved per page.