Cascades 519 handles checked baggage to Seattle from Vancouver. However, Vancouver is unusual in that you cannot check it early because the baggage must be with you during the US Immigration inspection immediately prior to boarding, plus the station is not staffed by Amtrak personnel. Baggage check is done trainside by the Amtrak train crew after US Immigration.
However, VIA's baggage room will day check your luggage and hold it for a fee ($10 CAD per piece, IIRC). You will have to reclaim all your luggage from VIA and have it with you before lining up for check in and US Immigration inspection (one line, you check in, then proceed through US inspection). You should know check in closes 15 minutes before departure so US Immigration inspection can be completed before scheduled departure. At VAC, you should really arrive no later than 45 minutes before departure and preferably an hour (I always shoot for 4:30 myself). You will probably have to line up to retrieve your day checked bags from VIA, too. During cruise season you won't be the only one doing it.
There isn't much in the way of food in the immediate area of Pacific Central Station, there's an A&W on the other side of Main Street by the Main Street/Science World Skytrain station (there used to be one in station, but it closed). In any case, you really cannot bring dinner onboard, unless dinner is crackers and mozzarella sticks. Most freshly prepared food will not be allowed past US inspection and they'll make you toss it. If you try to hide it and get caught, you'll be in for a possible fine and a note on your passport record that will get likely you pulled into secondary inspections every time you enter the US for a long, long time. Most commercially packaged snacks are okay (not meat products, though).
I don't have the current Cascades menu. It is the National cafe menu with some additional items. The Ivar's Clam Chowder is one they always have, and that's great.
VIA waives the day check charges to hold baggage for 519 for those arriving on the Canadian in Sleeper Plus or Prestige classes, BTW.