Assuming all your questions relate to PA speakers:
Pa speaker inputs are usually either jack or XLR input, so you would have to use a splitter and run a mini jack to jack from your soundcard(splitter) out to each of the speakers, although that won't give you stereo.
Active speakers do have their own amps in them, which is one of their disadvantages if you break say while you're on tour. Could be anything, and it isn't as easy as getting a different speaker, or using the spare amp for example.
You might find that a lot of active speakers have preamps built in. But you would have to check which ones they are.
Some PA speakers (the active ones) just require an IEC plug (kettle lead). Passive speakers however require an amp, and you would plug the input from your soundcard into the amp, and then run either jack or speakon to your speakers (depending on amp/speaker power).
Yeh. Active : amp inside. Passive: No amp inside. Passive require a seperate power amp. Which is a good thing and a bad thing. Depends how you look at it.
HTH
Adding to this, Passive systems will run Speakon (made by Neutrik's, so expensive) locking connections (2,4,8 pole available) between the amps and speaker as it's a more robust connector. XLR is common on Active systems and Jacks are rarely used (certainly not on commercial systems).
Balanced XLR/Jack connections (connectors/connections have a common shield/ground) tend to be used, especially between the rack gear (preamps, amps, effect units, limiters/compressor etc) and the desk/mixer. Although input sources, apart from mics, tend to be unbalanced (cd player, instruments, soundcard etc).
You also find the source (either from a cd player, or out of the desk/mixer) will hit compressors/limiters before it feeds the amp(s).
You also have
>Line Array< PA setups, which as the title suggests is an array of cabs (horns/mids) in a line. They tend to be used on big gigs/tours or anywhere where you have a big audience. A line array like
>this< will usually be flown (hung) at the front of the stage and are curved towards the bottom to direct the sound towards the audience closest to the stage.
And to gain optimal level/audio, it's not uncommon at the this level to find livesound engineers doing simulations (there are a handful of packages around) of the venue, at various capacity, to know what cabs to use and to get exact figures for cab position in the arrays/stacks.
On another note, you'll find majority of (high street, big Ibiza venues like Pacha with have a full blown setup) clubs are in Mono rather than Stereo as it saves on headaches with issues like phasing.
