1. To get to the Camden station, I would recommend taking the MARC train from Penn Station to Camden station. Penn Station is about 5 minutes away from the homewood campus, you can take a JHU shuttle to Penn Station.
Here's the shuttle schedule: http://www.jhu.edu/parking/jhmi_shuttle/homewood_jhmi_jun06.pdf
Since you live near One World, you'd probably want to go to the IFC stop. It looks like Penn Station is the 3rd stop. When you get to Penn Station, you would buy a ticket for the MARC train. This is the map:http://www.mtamaryland.com/services/marc/schedulesSystemMaps/marcTrainSystemMap.cfm#stations
Look to the top left for Penn Station and Camden Station.
2. Downtown Baltimore: not sure about this one, probably the light rail. I'm not sure where exactly you want to go, but you can check out http://www.mtamaryland.com/services/lightrail/schedule/06LightRail.pdf
for a map of stops that the light rail takes.
3. You could check out different neighborhoods in Balto that all have their own look/personality to them, such as Hampden (The Avenue), Mt. Vernon (short walk from Penn Station, little shops and lots of restaurants), Fells Point (lots of bars), Little Italy, etc. Usually I walk or take a cab. For places closer to school, lots of people like Paper Moon Diner (google it), the Charles Theatre (near Penn Station) and Thai Restaurant (not in the safest area but really good food).