The answer to your question is yes, but not for the reasons you suggest.
Runways are normally purpose built based on prevailing wind directions. This isn't always true though. Some airports may just be a runway placed in a convenient location based on terrain or local obstructions, but for the most part, it is prevailing winds that dictates the runway design. You want your runway to point in the direction that the wind blows most of the time, otherwise the runway could be effectively unsafe and useless if strong crosswinds are frequent.
For example prevailing winds in my region are almost always from a northerly direction (north or northwest usually), or when it's warm they are coming from the south. So the airport configuration is runway 13-31 and 18-36. We used to have a 07-25, but it was so rarely used that it got closed and developed into a new terminal and ramp area. Winds from the west are usually not to bad and runway 31 is ok. Winds from the east mean really nasty weather, and in that case most planes aren't gonna fly in those conditions anyhow (gale winds and t-storms). However with a north south runway configuration, 90% of the flights out of the airport are east or westbound. So you can see an east-west runway may seem like a good idea, until you consider that the wind doesn't often favour that layout in or region.
As for which runway is used for departing, it may occasionally be based on departing direction of the aircraft if conditions permit, but normally it is wind, aircraft type and instrument capabilities, and standard operating procedures of the control zone that dictates what runway is used for landing and departing (not always the same runway). For example runway 27 could be the active departing runway, but a pilot could request a different runway for convenience to get more of a straight out departure....not that the request will necessarily be granted, but it is certainly permissible to ask. Or a departure procedure for a specific type of SID is only available off certain runways so certain planes with suitable equipment on IFR departures would be using that runway.
Hope that helps.