How can I launch a new Terminal in OSX with a specified profile from the command line?

You can export your settings profile from the preferences window, then open the settings file with the open command. For example:

bash-3.2$ open "Documents/Man Page.terminal"

To run a particular command in the terminal such as a script called yourcommand stored in your bin directory, use 'export settings' from a terminal profile that you like to create a file with extension .terminal, then edit the .terminal file in a text editor and specify

    <key>CommandString</key>
    <string>/Users/youruserid/bin/yourcommand</string>  
    <key>RunCommandAsShell</key>
    <true/>

Then you can double-click or use the open command to run this and open a new terminal on this command.