Non-Linear Video Editor for Free or Cheap That Does These Things Background
I bought a couple of Handycams 6 months ago, and have since then been making videos and editing them and publishing them:

Sathyaish Chakravarthy  

Over the period, I have downloaded and toyed with plenty of video editors that are available free of charge. However, I cannot find a single editor that fulfills all my requirements. As a result, I am not able to make the quality of videos I wish to. Also, it takes up a lot of my time.

I am a sole proprietor of a start-up and time is the only asset I have, so being short of time and money, I cannot afford to spend too much of either of them on non-core activities, video editing being one (it's a marketing activity for me, my core activities being learning/studying for the corporate training programs I offer, preparing for them, conducting them, making sales calls, calling into people, etc.)

Until now, I have tried the following software:
1) Jahshaka
2) Windows Movie Maker
3) Avidemux
4) Free Video Cutter
5) Free Video Dub
6) AVI Edit
7) Blaze Media Pro
8) AVI Trimmer
9) t@b ZS4 Video Editor
10) Video Spin
11) Virtual Dub
12) Wax  

My Requirements
I require a non-linear video editing software that is either available for free or at a nominal charge (under $100) and allows me to do the following:

a) Use chroma key to change the background. Wax does it but I lose the audio in the output video file. I see it is a problem that many people have reported.

b) Edit the audio in the video file independent of the visual. For example, I may want to mute the audio for a couple of seconds, or replace the audio during a certain 4-second clip with a different audio file (mp3/wav/raw PCM in the audio editor).

c) Mix, append, insert at any point, another video from a different video file into the source video file.

d) Mix, append, insert at any point, only the visual from another video file into the source video file while having the audio of the source video file play for the duration.

e) Insert audio effects -- echo, reverb, generated sounds like bullet shots, etc. into the video.

f) Chop a frame of the video and split it into two vertical copies, one of which is transposed horizontally to create a lateral mirroring effect, and be able to edit each of the copies independently.

To explain point (f), please consider this.

I have a video of me sitting on a chair facing slightly towards my left. I want to take the frames from this video and flip them horizontally so that I now face towards my right instead. Then, I might want to slice each original frame into two vertical images -- the left one being the original image in the frame, and the right one being the laterally inverted/horizontally flipped image. Also, I want that one of the images, say, the laterally inverted image, be black &amp; white instead of color.

Question
Is there a non-linear video editing tool that is available either for free or for less than $100 to do all of these things?

Update: I forgot to mention that I am a Windows user.
Both kdenlive and cinelerra should do all you need. If you can't make them so, try the consumer version of Sony Vegas, it's also still in your price range.