1. In most cases, discrete sound cards have front-panel audio headers wired to the HD Audio spec, or in some cases, the older AC'97 spec.
2. It's just like connecting the LEDs, power, and reset buttons to the motherboard, along with USB port headers. You just slide the front-panel audio header over the exposed pins, making sure it's aligned properly.
3. All sound cards and other audio equipment have amplified analog outputs, so it's mostly a question of how well its amplification circuit is suited toward your particular headphones.
4. That depends on what you plan on doing with your computer. If you plan on gaming, X-Fi cards (except XtremeAudio ones) are more suited to that, but the Linux driver situation is pretty abysmal if you have the wrong card, to the point where you'd be better off with one of the numerous C-Media cards.
Since your X-540 speaker system requires extra analog outputs, cards like the X-Fi Titanium HD and Xonar Essence STX are right out since they only output two channels in analog.
The X-Fi Forte might be a good bet overall, provided that you make sure to get a newer card that comes with a heatsink on the DSP. If it doesn't, it may be from an older batch that's more prone to grounding issues and other nastiness.
If you would rather keep it cheap, there's the $30 Xonar DG. There's better cards out there, but in terms of bang for the buck, it's hard to beat, and it offers the extra analog outputs that most top-tier cards don't (save for the Xonar Essence ST, the PCI version of the STX that has an optional 7.1 extension card that isn't compatible with the STX for some reason).
I do have one warning regarding the front-panel audio jacks on most computer cases, though: most of them are rather cheap and introduce a lot of undesirable noise you're bound to notice with decent headphones like the M50.
