You can clear the private data(history,cookies,temporary files)in Firefox in three ways:
1. Press Ctrl+Shift+Del and the Clear Private Data Windows should come up and check all the boxes of the of the ones you want to be deleted then press Clear Private Data Now
2. Go to Tools scroll down and...
No the history,surfing,computer name or IP Address can't be seen by that person because those files are saved to your computer but since the wireless network belongs to them basically you have the same ip address so the only one who can see what you are doing on the internet is your neigbors...