While I am not familiar with Dwmail, I can answer some of your question about Dreamhost software and capabilities:
Dreamhost runs PHP version 4.4.2, 4.4.4, and 5.1.2 on their various servers- you can select whether to run PHP version 4 or version 5 "pre-installed" php.cgi versions for each domain hosted.
These pre-compiled versions of PHP vary somewhat in the modules installed. You can inspect the modules available in each installation from this Dreamhost Wiki article on PHP module configuration at Dreamhost.
Should you need additional modules, and if you are technically proficient with *nix shell operations and PHP, Dreamhost allows you to install your own "custom" version of PHP to provide whatever functionality you require.
The custom Dreamhost Control Panel does allow you to establish quotas per user and per mail account (whole account, not just inbox).
Dreamhost has several versions of MySQL installed - My servers are running 5.0.24 and 4.1.16 - Dreamhost has stated that all new MySQL database will be using MySQL 5.
While you have not specified exactly what "outbound connections" you are concerned about, DH allows outbound email., telnet, ssh, rsync, ftp, etc. - outbound email is limited to 100 or 200 emails per hour per user (depending on which method is used for sending), though DH hosted mailman mailing list are not so limited.
Again, without specifics of what you have in mind, a static IP or a dedicated server may or may not "fix" any "blocking" - you should contact DH Sales directly for precise and authoritative info on that.