Just a quick answer to your questions, I am sure others will respond also.
First, it is properly called a ship although you will hear both.
Although I have not been on the Westerdam, I have been on the Zuiderdam (same size). The wireless internet is only supposed to work in some public areas, but I have seen posts that it works in some rooms. The cost was $55 for 100 minutes plus a setup fee of I believe $15. There is also a dial-up available from rooms but I don't know the specifics. If you don't want to take your laptop there are plenty of public machines you could use for email checks and so forth.
Packing your suitcases would depend on how you are getting to Seattle. If you are flying it might be a good idea to spit as suggested. Once you are on the ship everything stays put.
Liquor is a subject of many discussions on ALL the cruise line boards. By rule you are not allowed to bring it aboard and if found in your carryon luggage it will be held for you until the end of the voyage. At least one poster on another board mentioned some being found during a checked baggage inspection and being held. Having said that, many posters talk about carefully putting bottles in their checked baggage.
Hope this helps, post other questions if you wish