It's cool that word of Starcraft is getting out! Although, I believe only 24 teams are going to playoffs, not 32 like the article says.

32 are going to playoffs :) but first seed gets a bye in the first round. check out the rules page

(Division will be seeded in the Round of 16, while the second and third place finishers will be placed in the Round of 32. The playoffs will be split by East and West Conferences, with the winners of each conference facing off in the Grand Final.)

So the #1 seeds will face a #2 or #3 seed in the 2nd round, or is it possible for a #1 seed to face another #1 seed in the 2nd round?

the #1 seed will face the winner of the #2 vs #3 seed round

I thought top 3 in each division got spots in the playoffs? There are 8 divisions = 24 teams..... Top team gets a bye, the other two face off, knocking the total number of teams down to 16.....

Or are 4 teams in each division going, with the top getting a double bye, and the #2 getting a single bye? ie, #3 and #4 battle it out to face #2, which battle it out to face #1, which is then the top 8?

I'm kinda confused.....

Impervious, you're right in your initial thoughts..
top 3 from each, #1 gets a single bye into the ro16, 2 and 3 battle it out, and then ro16 will be #1's vs winners from 2/3 matches.

Ro8 will be independent of any byes or anything like that.