If you buy a normal day ticket, yes, it is good at West, Central, Hyak, and Alpental.
If you're talking season pass, the unlimited Summit pass is good at all stated hills above (so yes, Alpental too). If you get the limited one or whatever it is, it is good at West, Central, and Hyak all days, but only Alpental during the week.
And yeah, when you buy a day lift ticket, you can buy it at any of the base areas, and it will be good at any of the base areas. There are cross-over trails to ski between West, Central, and Hyak, but in order to get to Alpental (on the other side of the freeway, and back up inside an armpit of a valley) you either need to drive over there, or take a Summit shuttle.