In April 2009, they had wi-fi, but for a nominal fee. It might be difficult to access without working knowledge of the payment system, i.e. Korean language and/or Korean credit card. If I recall, it was less than 3000 won for access.

I'm not sure about first class, but there are definetely no power outlets in the regular class. Seoul to Busan should be at or just less than 3 hours - hopefully you'll have enough juice. Also if you plan on doing the Seoul to Busan trip, it may be well worth it to buy a 3 day saver pass, even if you are only making one round trip.

BTW if you end up in a standard seat and feel extremely cramped, you can always try moving to the "jump" seat - they are located in-between trains.