DM probably refers to Darkness Message, which is just the Combine's in-game messaging system, accessed by clicking the envelope icon on your event bar at the top of the page.
For information on buying ships or any other assets, please read the Guide, linked at the top of each page. It teaches you how and where to purchase assets, and also walks you through how to travel.
Factions are companies and governments. They pay you credits and give you a free ship to use as well as something to do. The game is designed around them, so it is highly recommended that you join one, else you will probably get frustrated with the lack of progress and money and won't have anything to do.