Is it possible to moderate New User Requests?

Under Authentication in the Administration Panel there is an Account Activation Mode setting.  Setting that to Admin Approval will require each account be approved before being able to log in to the site.

Is there a way to block certain email addresses that are known to be spammers?

If they are an existing user, you can set their account to Disapproved and select to hide all of their content from the community. This way the email address cannot be used to sign up again, and their posts are stopped. 

If they are an existing user, you can set their account to Disapproved and select to hide all of their content from the community. This way the email address cannot be used to sign up again, and their posts are stopped.