Without seeing the bike in person it is impossible to know if the wheel isn't inserted fully into the fork ends making the wheel look offcenter in the pic, or if one or both of the fork legs are bent, or if the wheel is bent/warped and the pic just happens to have been taken with the wobbled section between the forks.

The chrome looking portion is the lower headset cup (I typo'd before) which is pressed into the head tube. Experience is the best teacher for knowing if something might be messed up or if it just needs fresh grease and adjustment or replacement. To me it looks like the bike "might" be in original condition, as in someone bought it new and never changed anything on it over the years except for maybe tires and tubes and maybe brake pads. The only way to know for certain before buying it is to remove the seatpost and looking down inside the seat tube, and also removing the handlebar stem and looking down inside the headtube. And while those parts are off you might want to turn the bike upside down to see if any water drains out (I did this to a bike I bought once and about two cups of rusty water flowed out of the seat tube, that one took a bit of work to clean/fix up).

Spend some time on the ParkTool and SheldonBrown websites to get more familiar with bike components and how to repair them, it will help you to know what to look for.

To me, if I were to get the above bike, I'd plan on having to give it a complete overhaul and rebuild. But there is no way to know up front if you'll need to replace bearings and such until you get things dismantled and cleaned up. Most of the bikes I work on simply need cleaning and fresh grease since most people put very few miles on their bikes, most still have their original tires on them regardless of how old the bike happens to be, so apart from corrosion the bearings/races/cups are rarely worn out in most cases.

Hope this helps some. It might very well be a nice bike that just needs some soap and water, or it might need more attention than that, only way to know for certain is to look at it in person and see how things look and feel.

edit:
click here: http://www.parktool.com/blog/repair-...eadset-service

They are calling the cup a race as well, but I tend to call the male portion a race (where the bearings run outside of the surface) and the female portion a cup (where the bearings run inside of the surface area). Helps me to differentiate what I'm talking about. Some of us here do our own work, some take portions of a job into a shop to use the shop's tools where more expensive tools are required.