It can do basically everything you're wanting to do, but you may have to do it just a little differently than you're used to.
1. Podcasts and MP3's will be handled through iTunes on your Mac Mini. It's free.
2. When you get it setup you'll simply download the Kindle app (also free) and log in to your Amazon.com account. Through the app you will be able to download or archive any books you've paid for.
3. Not exactly sure what you're asking in the last question, but I'll answer in two ways. To answer it one way, if you already have a stereo system of some kind, then yes, you can run a 1/8 inch male cable out of the iPad's headphone jack into the Aux of the stereo. Some Aux inputs also use a 1/8 inch cable and some use RCA. You'll just have to get the right cable.
To answer another way, if you don't have a stereo already and want the iPad to be your primary music device then you'll need to get some external speakers. The built-in speakers are fine for holding the device in your hands and watching things or listening to something quickly, but it won't fill room. You can either buy regular computer speakers and hook them up to the iPad, or buy a specific dock made for the iPad. The latter is more expensive, but if you're a true audiophile they typically sound better. Plus the docs are made to charge the device while you're playing music off of it.
Finally, I've known many people who've replaced their laptops with iPads. It all depends on how much you do. The iPad is great for web browsing, videos, music, emails, Facebook, and doing other lighter tasks. There are good MS Office-type apps that cost a bit that can reasonably replace your laptop. If you plan on doing a lot of typing, then I'd definitely recommend getting a compatible Bluetooth keyboard. They run about $60-100 depending on if you want it built into a case or not.
Hope this helps.
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