Mondo questions!  Some answers.  In all cases I am assuming direct-to-mixer connection.

• Output mode should be 'Studio Direct'.  Generally full amp models should be used along with Cab Models and Mic Models.  
• Stereo:  this depends on the mixer and whether it allows you to pan left and right to separate speakers. 
  • You would need to connect both left and right outputs (1/4" or XLR)  from the Pod into two channels on the Mixer
  • Use the Pan on the mixer channel to pan the left channel to the left speaker and the right channel .....
  • This assumes that you have a Stereo preset .... if you are using mono effects thoughout then you will not hear stereo!
  • Stereo does not always work brilliantly in a live context.  Good mono tones are more consistent if you can live with them.
• Ignore the L6 link unless you have a Line 6 DT25, DT50, Stagescape Mixer or Stagesource speakers.  It does nothing with non-Line 6 gear or older lLine 6 gear.
  • If you want to know more about the L6 Link then run queries on this site.

The basic question of whether your sound will be like headphones.  The simple answer is probably 'no' because the sound changes when it gets scaled up to go through a PA.

If you can get access to a mixer and PA beforehand to checkout your presets then you would be well advised to do so.  Each PA will sound a little different but you can get all your tones into the right ballpark with a rehearsal room mixer or similar.  With that said - don't panic, just be ready to tweak your tones .... and volume levels. EQ on the mixing desk is your friend.. 

Try and restrict the number of presets you use initially until you are happy with them - less tweaking to do in a hurry !