In your folder pane (down the left hand side of the Thunderbird main page) there is an optional toolbar where you can display total and unread numbers.

In the past you'd have to look for a tiny square button at the top right of this folder pane to set the items to be displayed. IIRC, in current Thunderbird, you go to View|Toolbars and select "Folder Pane Columns". There is also a Folder Pane toolbar with provides a handy drop-down in the folder pane for selecting the folder view.

For your mailbox capacity, you need to ask your email provider. Look for their web page and there will be a way to log in to your email account there. If they don't actually display this information, there should be links to help you find it, or to post a query to their user support personnel.