Canon 600D/ T3i Video Output and Converting?
The default video files made by most Canon DSLRs is an H264 video file in an MOV container.  Decoding high definition video at the data rates that most Canon cameras use is intensive for both memory, disk and CPU unless you have a dedicated decoder chip.  Your iPod Touch uses flash storage (which is fast) and has H264 decoding capability to make it run smoothly.

On the other hand, a lower end desktop in particular is going to have slow hard drives and may not have sufficient power to decode the file on the fly, thus resulting in lag during playback.  Based on the quality level you describe, data retrieval from disk is most likely the problem you are experiencing.  So now with some groundwork set, lets move on to your direct questions.

1) It isn't necessary to convert video you shoot from your T3i.  It's a standard format and will play or be editable on any system capable of playing it.  If you are having issues with the H264 playback lagging on a particular system, you can try converting it to a lower data rate or less CPU/Memory intensive compression. 

Either of these options might make the issue worse if you go in the wrong direction (for example, most algorithms that are less CPU intense take more space and vice versa, so if you were CPU limited and you use a higher compression, it might be more jumpy).  You can also simply sacrifice quality to make it play faster and take less space, but this isn't really ideal.

2) Any good transcoder can do the job.  The files that come off the camera are generally pretty high quality and thus should transcode well.  Your choice of encoder depends a lot on the platform you are on.  FFMPEG(MPEG based formats, including H264) isn't that user friendly, but is freely available and works cross platform.  Other options include the free Windows Media Encoder(WMV) on Windows, Quicktime(several formats) on Mac or Windows, Adobe Media Encoder(numerous formats) on Mac or Windows or Microsoft Expression Encoder(WMV).  

The basic key for quality conversion is to keep the native resolution (number of pixels) in the video and use a high enough data rate to support the quality.  VBR 2 pass is better than VBR 1 pass which is generally better than Constant Bit Rate, but each takes more time than the latter to encode.

3) Video is BIG.  Really, REALLY, BIG.  Since the camera needs to record fast, fairly limited compression is used.  It sounds like you are probably using All I frame video which is fairly high data rate video.  Keep in mind that you are effectively storing 24 pictures every second, continuously.  If it was truly uncompressed, it would go even faster.  RAW, uncompressed HD video produces 261 megabytes of information PER SECOND! (14 bits per color, 3 colors, 1920 x 1080 pixels per picture, 24 pictures a second.)  Makes 10 minutes on a 4GB card sound a lot better doesn't it?  

If you don't need as high of a quality, you can use IBP frame video which will drastically reduce (about 1/5 to 1/6 the size) the amount of space required though it also drops the quality of the video.