To copy or paste text you can use keyboard shortcuts. Use CTRL + C to copy (press both keys at the same time when text is highlighted) and CTRL + V to paste. You can also use this for images if the email is in html format. To add any other type of attachment you need to do it through the "Attach" menu.
To open /save attachments you should use left click.
If the right click is not working in general, not just in hotmail, then this is a separate issue. I sometimes have this issue, cleaning the pc of all cookies and offline content fixes the problem (in Internet Explorer do this by going to Internet Options -> General -> click the "Delete Cookies" and "Delete Files" buttons.