1) Carousel is only compatible with a select number of professional telephony boards. You will probably have to check with NCH to be sure, but I doubt your current modem is compatible.
2) Yes, that is the correct product. The SPA3000 and 3102 go for around the same price despite the fact the 3102 has a built-in broadband router (about the only major difference). They typically sell for anywhere between $80 - $100 new depending on where you get them from.
Note that most big retail stores (e.g. Target/Walmart/Best Buy) probably won't carry the item. These retail stores tend to sell consumer products that are easy to use and configure for the average person. This product is more for advanced users, experts and businesses who have a good idea of what they're doing and exactly what they need the product for. You're more likely to find these products in lesser known computer stores (the type where the service isn't that great, and you're expected to know what you want), and online stores.
Take a look here for a bunch of online stores (which may also have retail stores in your area) that sell the 3000/3102: http://www.google.com/products?q=SPA3000+O...=1&ie=UTF-8
Just a word of caution before you buy: I won't lie, it is not simple and easy to get working and there is no wizard or guide that comes with the product that will help you out either. That being said both NCH and myself have written step-by-step guides for setting up these adaptors. As long as you follow the instructions, it should be relatively straight forward to get working.
3) Using Uplink incoming calls from Skype can be routed to Axon just as if the call came in from your regular phone line. Also outgoing calls can be put through on Skype to save money, although I recommend using another VoIP service for outgoing calls rather than Skype.