The NPC Market (Market link on the right menu) is only accessible through Commerce Centres, meaning you need someone to give you access to one. Generally they don't have much for sale, though, and if you're interested in buying and selling, the Trading section of the Guide (linked at the top of every page) will be more useful to you.
You should have no trouble traveling around the city once you have exited the facility you start in. What are you having trouble with? To leave the planet you will need to join a faction who will have a ship for you to use.
Weapons can be found in NPC shops which are located on all race homeworlds. Note that since the Combine is still being developed, combat is not yet possible against other players, only against brawler NPCs. Therefore, weapons don't have any functional use just yet.