What sound card + sound server are you running? Skype is well known for causing problems, as you can often only have one application accessing your audio device at a time depending on your system. Check the Skype support site + forums, as they detail covering this problem in detail which should resolve your first + second issue.
As for only receiving audio through your headphones, have you double checked the mixer settings to ensure you have audio turned up? Are you able to play audio through amaroK to play correctly through your speakers? If so, seems a bizzare Skype issue, but more likely back to mixer settings.