Noob to AMP/DAC's....few questions

Sorry if this stuff is too basic for you, but here goes:

You can get either a standalone dac and a standalone amp, or a combo dac/amp.  A dac is a digital-to-analog converter, meaning it takes a digital signal from your computer or other source and converts it to an analog waveform.  Your amp would take that analog signal and amplify or attenuate it as appropriate for your headphone.

The digital signal can be passed by 3 common methods, USB, optical, or coax (rca).  Each method has pros and cons, but there aren't huge differences so I won't go into them here.  A lot of newer motherboards can deliver the digital signal by all 3.  Any method will work fine as long as your dac has the appropriate input.  Basically you're bypassing the computer's D/A conversion with the expectation that a standalone dac can do it better.  So in a nutshell, computer -> dac -> amp -> headphone.

Alternatively, you can have your computer handle the digital/analog conversion, and just pass the analog signal to an outboard amp.  In your case it sounds like your sound card would do the D/A conversion and then output analog for an amp.  If your headphones are difficult to drive, your sound card may not be up to driving them, so this is where a standalone amp is beneficial.  Computer -> amp -> headphone.

If your computer speakers are self-powered, i.e. contain their own amp, you just pass an analog signal to them.  They won't need your dac or amp.  If you get a standalone dac, you can use the analog output for the speakers as well.

It's hard to say whether a dac or amp is going to improve your sound.  If your HD555 are being optimally driven by your sound card, then you won't hear any benefit.  I haven't heard your headphone or sound card, so I'm not sure.

An external dac would benefit both headphones and speakers.  Remember the dac is creating your analog signal, so if it's doing a better job of that, then you'll hear it through both headphones and speakers.  An external amp will not benefit self-powered speakers (which is what I think you're talking about), the speakers already have an amp built-in and probably cannot accept external amplification.  And in any case, most headphone amps can't drive speakers anyway.

It sounds like you have a high-end sound card.  If you're happy with the sound card, it's quite possible you don't need to upgrade anything.  You might have to spend a LOT of money to get a noticeable improvement.  If you have a $300 sound card, I'd imagine your D/A conversion is pretty good.  You could probably skip the external dac.  The headphone opamp could be decent as well, and/or your headphones are easy to drive.

If you want an upgrade, here's what I'd do.  Do some research and find out what amp will work well with the Sennheiser.  Don't worry about the dac for now, just get an amp.  Buy it from someplace with a good return policy, or used so you can sell it for minimal loss.  Try it out for a while, see if you're happier with the amp, or with the sound card.