The sides are plywood with an Oak Laminate (ie., Laminated Plywood.) You can buy this in sheets of 4x8. It's expensive but cheaper than 1/2" solid oak (and lighter in weight.)
Yes, the external doors and FRONT face are solid oak. (Again, the sides and back are laminated plywood.) Of course, the INSIDES and OUTSIDES of the sides and back are laminated with oak. Moldings are solid oak. One thing to consider (speaking about moldings) is our TOP will have a Crown Molding. The TOP of the molding will be 'even' with the TOP of the cabinet. This way, my wife can put 'things' up there and they won't look like they're sitting 'INSIDE' of the crown molding. Do you know what I mean? You will then have to account for this measurement if you go this route. The other option, of course, is to attach your molding at the top-edge of the Armoir and let 'things' sit 'inside' of the crowned top. There will be a decorative 'skirt' at the front and around the 2 sides.
As for a biscuit joiner, Home Depot has a DeWalt for about $210. My Dad is looking at it as we speak. There are other brands but I guess it depends on how much you'll use it which will help you decide how much to spend, if at all. I don't necessarily think you're way out of your league if you have the room, the tools, and the time to make it. DO make your drawings and don't forget to account for the thickness of the wood AND the laminate (where it's being used.) I hope I didn't say too much. I wish I could build the bloody thing! (I'm a bit jealous you're doing one.) Again, stick around a little while to see if anyone else adds to your post. If you need any more info, you might want to consider e-mailing me directly as your post is getting 'buried'. (After a while, it gets hard to 'track' people's posts since there are so many of them.)