I never went through a group interview with SkyWest (and I have never worked as a customer service agent) but I do work for SkyWest in Denver and I have attended one group interview where I spoke to the group and answered questions so I could probably give you some info.
First I'll answer your questions: I think they are about 4 hours or so. I would probably take the whole day off work just in case. I know they give a big presentation about the company, have some supervisor or manager talk about the position and answer questions (which is what I did) and then I believe they have one on one interviews. I suppose you don't HAVE to dress nice but the couple of people who show up in jeans and a t-shirt end up looking like idiots and probably don't get hired. Dress nice for all job interviews. It can take quite a while with airline jobs from when you get "hired" to when you actually start working. For me it was about 2 months (which I know was longer than average). There are all sorts of fingerprinting, background checks, drug tests, etc. that take a while to go through. I would figure about a month on average.
Now a little about the job: You see it is part-time right? SkyWest is only hiring part-time people in Denver and that isn't likely gonna change any time soon. If you are actually planning for this job to be your main source of income look somewhere else. We were short-staffed for years and there was always an endless supply of overtime which made it possible to make a decent living here but that is no longer the case. I know ramp part-time is scheduled for 20 hours a week but I belive CS is even less. There are NO extra hours to be had. Part-timers don't get benefits (health, dental, etc.) or vacation hours.
Now... if you have another well paying job with health insurence and just want to do this part-time in order to make a little extra money, get your foot in the door with an airline or travel a lot then I wouldn't have a problem recommending it. SkyWest employees in Denver have excellent travel benefits (better than any other airline at DIA). Non-reving is increasingly becomming more and more a pain in the ass but you certainly have lots of great options working here.
Well, I rambled on long enough, if you have any questions feel free to PM me. I know lots of the recruitment people and I could ask them any questions you have.