I you got to the Adobe Audition site, you can download a free trial of Adobe Audition. The demo itself does everything you specified, (multi-track recording and playback, , linear and non-linear editing, and much more.
After you've played around with it, Adobe does offer a "download" option for people who want to buy it.
I trained on this, I work with it at home--I'm pretty sure it will do what you want.
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