You will have to see if your sub box already has an amp with it or not. If it does then you don't need another one, unless you are using it to run other speakers.
Then you will have measure across one of the hole(s)(the longest part of the hole) where the speaker would go in your sub box and see if it is the same size as the Kicker speakers.
As for the stereo, it all depends on the type of amp you have or are going to buy. Most amps take RCA type inputs, so your stereo unit will require RCA out if so.
Hope this help you to make some BASS!!!