Where does IMovie store clips?

In iMovie '06 the clips are spored in the "Media" folder within the "project" package file. In iMovie '08 they are stored in the named events within the "iMovie Events" folder. In both applications the "trash" is merely "marked" as such and remains physically part of the clip until the user tells the application to physically remove the marked or rejected clips/frame ranges. In iMovie '06 this is done by "emptying the trash" from within the application (i.e., deleted by re-writing the clips) while in iMovie '08 the command is "Remove Rejected Clips to the Trash" in which case the media is placed in the regular trash can.

When it says "View the trash?" where on the computer is that trash located?

It is looking at a "virtual" file that represents the material marked for deletion. Until physically deleted, the material "marked" for deletion remains a physically part of the imported clip.

I would like access to these files outside the program.

Then open the original clip, the media is still contained there. If you open the Timeline clip and the media clip at the same time you can compare the files and actually see wis marked for deleting but still present.

Can I change what disc iMovie saves these files to?

Yes. In iMovie '06 you can select the destination drive at the time you create the project. In iMovie '08, you can select the destination for your events each time you import media.

How do I get it to save all the files, trash or not, to my external disc and not my computer's hard drive?

In iMovie '06, project are self-contained and can be move independently at the "Finder" level. Double clicking on a project should automatically open the parent application as re-establish the "recent" path for navigation purposes. In iMovie '08 you can move events between event folders within the application by merely "dragging 'n dropping" them. This will update the internal database.

The project is a "package" file. "Control-Click" the named project file and select the "Show Package Contents" contextual menu option from the list. This will open the package as a "folder" which can then be navigated in a normal manner.

This, of course, depends on your definition of "good enough quality." I use a single file for iPhone, iPod, TV viewing on a 42 inch Panasonic HDTV. It is a standard H.264/AAC file iPod profile but with an extra 100 Kbps of headroom allocated rather that pushing the 1500 Kbps video data rate limit. I am in the process of converting my entire VHS/DVD collection of media ranging from movies and theatrical serials of the 1930's through broadcast TV between the 1940's to present, as well as, current blockbuster movies.

And is there a way to play back video from my hard drive to a TV?

I believe the are several devices that will allow you to do this but my only experience is with the TV device from an external 1 TB LaCie drive attached to my G5.

I want to save as much video on the drive as possible but still have good enough quality to play back full screen.

Apple's iPod reset is will produce movies with storage requirements on the order of 12 MBs/min. While I have used QVGA files with a 512 Kbps combined (video + audio) data rate (i.e., about 4 MBs/min), i generally find this quality marginal, at best, for "full screen" viewing.

Yes. The H.264/ACC compression combination has an exceptionally wide range of use. It is modern, highly efficient, and very scalable. For any given file size it normally provides the best quality or for a given level of quality will produce the smallest file.
Depending on my work flow, I use either MPEG Streamclip, QT Pro, iTunes, or iMovie. All of these applications have an iPod preset. MPEG Streamclip's preset allows manual user modifications while Apple's are, for the most part, contextual in nature and do not. If you want your files to be device capable, it is usually best to use these presets to ensure the correct MPEG-4 or MPEG-4/AVC profile is used. If you only want data rate compatibilities, want to use filters, and/or want to access optional user settings like "B-frames", etc. then you can always use QT's full manual work flow options.

I'm not sure what you mean by the extra 100kbs allocated.

Apple contextual presets are targeted for 1500 Kbps video and 128 Kbps audio to stay within iPod device limits which are error trapped before allowing iTunes to transfer files to an iPod device. I generally target mine for 1400 Kbps video and 128 Kbps to provide and extra 100 Kbps of headroom since many of my files don't fit Apple's concept of an "average" source file.

When I call up this compression type I am given the following options - Quality High or Highest, Encoding - Best Quality, Frame rate (29.97fps), Data Rate - Automatic, Size Compressor native 720x480 and there are some filter options, none of which I use.

I don't normally recommend the use of full manual compression option unless the individual knows the use of each control and how it relates to the use of other controls. There are simply too many misconceptions floating around. E.g., some people seem to think that if you cut the frame rate in half, this means you can cut the video data rate in half and still improve your quality. (Nothing could be further from the truth since the data per pixel per unit of time ratio remains constant here.) The work flow I suggested lets the application choose the proper settings. E.g., you don't to worry about things like device native since the device work flow should take care of these questions. (I.e., an NTSC DVD will be re-encoded for 720x480/853x480 use while monitor, DVI TV, external scaling devices like TV accept "square" pixel inputs directly.) Generally speaking, you never want to change frame rates if you can avoid it, overdriving the "quality" setting can cause data rate excursions to exceed ±250% of your target data rate (e.g., for an iPod target of 1500 Kbps this means you could see instantaneous data rates on the order of of 600 kbps to 3750 kbps in the multi-mass mode) which can effect device compatibility, and use of "highest quality", A.K.A. the multi-pass mode, can more than double your compression times. Dimensions for your files are determined by the Aspect Ratio of you project and your particular output work flow. For instance, a 4:3 project will create a 640x480 "Medium" or 720x540 "Large" file; a 3:2 project will produce a 640x424 "Medium" or 808x540 "Large" files; and a 16:9 project makes either 640x360 "Medium" or 960x540 "Large" files. With regard to the "Automatic" data rate setting, this allows the application to set the data rate as needed depending on the quality, detail, lighting, etc contained in the source file. An SD file of high quality may produce a file whose data rate may be on the order of 18.0 to 20.0 Mbps -- not probably what you have in mind for a "small file of reasonable quality."

In addition Fast start - prepare for internet streaming is selected. How would you alter those settings.

The "Fast Start" option allows certain files posted to the the Internet to begin playback while the file is still downloading once a sufficient buffer is established. It would not be required for playing files from your computer on your TV. The actual "Streaming" file options only apply if you use a real time (RTSP) server. So, if you don't know what this is, it is safe to say you don't need them and, once again, they do they apply to computer playback on your TV.
My basic advice would be to use the iMovie presets here. Use the "Medium" option for SD or HD files which are to be played on your TV or burned to DVD. If you are using HD sourced material and you find the quality less than you want, then switch to the "Large" format. Doing this will increase your target data rate from 1.7 Mbps to 4.0 Mbps (roughly a 235% increase) while only increasing your picture area by 125% to 150%. Thus, you should see increased quality in terms of detail, better separation between foreground and background, better motion prediction, etc. Basically, all you have to do is determine which preset option to use for any given project source and target use. This is what I was referring to when I indicated that the concept of quality is really a matter of personal perception.

Possibly. Depends on the specific work flow you are attempting to use. For instance...
1) If you are trying to use one of the "Share Menu" (iTunes..., Media Browser..., You Tube..., or ,Mac Web Gallery..." or "Export" (Export Movie...) options, then this is what you should see:

2) If you are using the "Export Using QuickTime", QT Pro "Export", GarageBand "Export to Disk...", then this is what you should see (note that there are not user options available here):

3) If you export your project to another compression format and later decide to convert it using iTunes, then this is what you would see:

Any of these options should access the same QT preset to create an iPod compatible file which will play on your TV via TV (or a similar home entertainment interface device accepting QT compression formats) and play in a manner similar to the way they play on your monitor if you use a DVI connection (i.e., without TV line input scaling or aspect adjustment options).