1. If you own a ship or are lent a ship by another player then the ship will always stay where you leave it, regardless of if its in a spaceport or in the middle of a field.
2. If you go and have a look at the factions pages there are several factions labelled as markets. If you are in one of there commerce centres, which they list on there respective websites, then you can buy off the NPC market. You can buy from the Centrepoint market, and one or two other markets, without being in any building. Imagine it as a sort of ebay.
3. The only sure way to earn CP's is the good old banner clicking, ie click the number next to where it says CP on the information tab and go to support the combine.
2. Trading stations and Commerce Centres must be built by players/factions. There are quite many around. You can either try looking at a few systems to spot trading stations or check with trading factions for Commerce Centres (they are the ones who can build them). Note that not all of them might be public. Centrepoint Station itself is not open to the public, so good luck getting in there.
The market sites Lesley was talking about are not connected to the NPC market and are, as said, sort of like ebay. You will have to talk to the actual seller to finish the deal and get the bought items. Make sure you follow the market's rules.
3. CPs can be acquired through banner clicking or helping SWC. To help SWC, please take a look at the Contact Us page (available from the top menu) and contact the leader of the team that best suits your skills.