Well, I was hoping someone who actually went to UW recently would chime in here, but I guess I will have to do for the time being.
I want to preface this by saying I did not attend UW, my children did not attend UW and I have never been in a sorority BUT we lived in WA for quite awhile and my kids grew up there, so around 40 of my daughter's friends attend or recently attended UW and probably 30 were in sororities or fraternities there. What little I know (and it is very LITTLE) is based on that.
The first thing anyone on here will tell you is to do the following:
1) Call or email the Greek life office at UW and ask them the questions you asked here.
2) Talk to friend or friendly acquaintances you have who are in sororities and ask them those same questions.
3) Go on the sorority websites and public FB's for those that have them. Find out about the sororities (just like you would find out about a company you want to work for). Pay attention to their GPA requirements and their avg GPA (above their average is what you're shooting for).
So having said that....UW is considered competitive for the NW and probably fairly competitive for the country as a whole. They have a large number of girls going through every year (1000 to 1200 on avg I believe) but also a large number of houses (16) since it is a big school. The good news is, out of 16 you will probably find many you like, but they have to like you too, so you need to keep an open mind and not cross anything off the list based on a first impression (kind of like dating).
It is LONG week. They move into dorms on Friday, go through recruitment all week, and move into houses the following weekend. You do get a two day break before school starts.
I THINK (not sure) that all 4 schools in the region (UO, UW, WSU, and OSU) have guaranteed bids. This means IF you go all the way through the process, IF you maximize your options, and IF you sign a preference card, you will get a bid somewhere.
That I know of, none of her friends had recs. That being said, particularly if you are a sophomore, and if you know alums already, get one. Again, it is like a job - why not do everything possible to have an edge? On the other hand, do you need to go through alum organizations and get 4 recs to every house - no. This is not SEC competitive.
The most important thing you can do is have a high GPA and be active. You will be competing with girls who all had pretty good ones and probably pretty strong resumes on top of that.
A sophomore will face heavier cuts than a freshman, so don't take it personally when that happens. It doesn't mean you won't get into a house, it just means some houses can take all freshman and they will do that.
I can't speak to the dress code issue. My daughter didn't ask for a daily "what I wore to recruitment" bulletin from her buddies (LOL), but I would guess that due to the time of year it falls (September) it is probably somewhere in between WSU (August/sundresses every day) and UO (October/jeans and cute shirts/1 dressy night). Ask your friends and the Greek life office.
On a good note - All of my daughter's friends were/are very happy in their houses, and I think they were spread out through 6 or 7 of the 16.
Sorry for being so long winded. Good luck and let us know how it goes.