I don't own any Schiit amps but some general responses to help you along as soon as possible:
1. AFAIK, it should have come with a power cable terminated with the plugs compatible for your country/continent.
2. Yes, one thing at a time. Like I said I don't have any Schiit amps, but as I suppose this to be your first desktop amp, I can chime in as I've been into full speaker rigs and now into desktop audio with headphones. I have an LD MkII at home that used to take the signal from a DAC-AH fed by my computer'sdigital out; then when that fried the digital receiver chip, the amp went into my bedroom to go with my Marantz CD60 (it had its own hp driver that does well enough for most cans); then I got a SuperPro 707 DAC for the PC and put the tube amp back to the computer rig.
3. You can, but honestly the signal might not maximize the Schiit's input, which were probably designed with fixed-voltage signal in mind. Meaning a true line out signal. 3.5mm to RCA is OK, I suppose, barring ergo issues. Personally, I just don't like cables getting in the way, like when you lift up an S:Flo or HM801 to change tracks, as opposed to a proper dock for an iPod, DAC or CDPLayer. Don't let that stop you though if you have a good line-out signal source.
4. Check DAC dimensions on manufacturer websites, but personally I'd rather not stack some desktop components. They get hotter than portables and unlike most photos of home speaker rigs, especially from manufacturer websites promoting a product line, most of these run Class A/B. Generally a 55w/channel A/B speaker amp can run a lot cooler than even a Class A tube preamp/headphone amp, and also because the compact headphone=gear designs use the chassis as the heatsink. Meaning just because the Lyr is on top, doesn't mean the heat it takes away from it's internal components won't make it to the chassis of the DAC which is probably trying to do the same thing.
5. Not necessarily, but if you get cables better than the freebies from either the amp or DAC or dock, I say you don't need anything really expensive. I use pro-audio 3-core conductors and terminate them with good quality plugs. If you don't have the DIY skills or quick access to someone who does, first thing you look at is the quality of the plugs. Weight, solid feel, and difficulty in pulling htem out are good (but not hte only) indicators; I had some entry-level Neutriks lose grip within a few months. Their ProFi line is fantastic though.
6. You don't need a "stereo." People use the term to refer to the whole rig, but it really jsut means, basically, 2 channel. As in your having two good eyes is also "stereo(scopic)" as much as your ears and the recording on most media are. That also means you don't need the entire "stereo rig," just the CDPlayer or DAC. One thing to consider though: Do you still listen and JUST listen, and swap out discs, or listen to each disc from start to finish? If most of these is a "no," you're much better off with a DAC with a USB input. Most DACs can get the same quality sound as a CDPlayer, barring a particular CDPLayer that you happen to like and there's no DAC with a similar circuit around. And I don't want to get into it, but there have been looooong threads on virtually every forum debating whether an optical drive inside a CDPlayer or a dedicated CD transport is better than a PC soundcard with SPDIF output, not to mention some with only USB, but generally, try not to worry too much about this part. Just upgrade your soundcard later on if you don't have SPDIF now, listen to music, and if you really need to sweat over details, it shouldn't be this one.
7. Just get a good source and of course a proper headphone that actually needs the juice the Lyr can deliver. You already have the DT880, no need to rush getting another headphone yet, so decide on a DAC or CDPlayer first.
One tip though, maybe you can start long-term gear planning already. The Fiio X3 portable player with SPDIF coaxial out is due next year, so a DAC might be a better choice. Just make sure it has more than one SPDIF input and a USB input, that way you can hook up your laptop through USB, or your PC through optical or USB, then instead of a CDPlayer, use the X3 when you don't need a computer's other functions.
