A mic preamp boosts a mic level signal up to line level. Sounds like a pretty simple operation, but it can be critical to your sound.
Compressors decrease volume by a user defined ratio over a user defined threshold. You do not plug a microphone into a compressor, although you may wish to put a compressor after the mic preamp to help tame your levels. A "channel strip" is a combination of a mic preamp and typically a compressor and EQ, so sometimes you can find compressors combine with mic pres.
A mixer mixes multiple audio signals together. Most mixers do have microphone preamps built in, but you don't need to get a mixer to have preamps....you also don't necessarily get preamps with a mixer.
There are no mic inputs on the Audiophile 2496...like most soundcards, it has two line level inputs. The Audio Buddy is a microphone preamp with two microphone inputs and two line level outputs.
To connect the audiobuddy to the audiophile, you'll need either 1/4" TS (phono) to RCA cables, or XLR to RCA cables (if the audiobuddy has XLR outputs, I'm not sure off hand). Basically it's just a connection issue because the Audiophile uses RCA connectors which are more common in home audio gear than recording gear. Since both the audiobuddy's output and the audiophile's input are at line level, it's just a matter of getting a cable with the right connectors on each end (or using adapters on existing cables).
Slackmaster 2000