If you use a free solution like Flowplayer or JW Player you then indeed have most freedom, and much more possibilities for a custom solution. As you guessed, it will eat lots of bandwidth, and might end in bad user experience if your servers have problems with streaming, or is just the typical shared hosting, is slow, etc. I would go with this solution if paying for great streaming servers, or my audience is very small and I need very special customization, branding, flexibility, etc. A big con is you actually add an extra step, you will need ffmpeg, mediacoder, Riva encoder, or any other, to encode you avi or whatever to flv format. This players are actually SWF "players" that actually playback your flv. Playing the vid as just a single SWF video file is not optimal neither stable.
I would go this way. Besides is simple to use, you don't have to care for bandwidth, it has an amazing amount of visits a month (that does not mean your video will have lots of visits, but will be in a place where lots of people go to check/search videos), and specially if need to upload often, the cost of time also counts. Its uploader has improved in speed, and you can customize how it shows also more than before. I tend to prefer to upload mp4 files saved with .h264 codec, as makes hi quality but small videos, and seems to work well with Youtube. But the site supports practically all formats available.
I also like Viddler.
The crossbrowser matter is not an issue with a custom player like JW or Flowplayer, as they are actually SWF, flash files; cross device is more of an issue. Because iphone and ipad, etc, till what I know, wont support flash. Youtube has did solved as plays videos alternatively in html 5, and that is transparent for the user, wont notice, as far as I know.
Your youtube questions.
1 There are a pair of tags to control both in typical playback url, as well as in embedded html syntax, to control the start time of a video. You have the option of adding pre rolls, post rolls, and midst rolls. I am not sure on how much flexibility you would have for that, and if indeed this might be a show stopper for you, and would need to choose the FW or Flowplayer option for this specific matter. Youtube has quite many tags that you can add to the url of embedded and normal versions, which people are not aware, and that allows quite extra control. Might not be enough for your needs, though.
2 Ranking will not be neededly affected. You might have more traffic for doing it in Youtube, but it might not happen so. Google is evolving more and more to make people focus on content. The key is content, and have backlinks of related content. Related to that kind of content. Ranking is not the same than traffic. And there is a possibility you get some nice traffic thanks to youtube. But unless you make a great hit video, it might just end up as a little more help, not more.
3 Youtube should play in iPad for the html 5 playback capability it has. If does not work with certain code, not sure. Seems works, for the latest iOS 4.x . You might want to check this
4 There are some ways to monetize from Youtube videos. I am not sure if it's a great way, though. For that, you might also give it a try to alternative sites with better solutions for that specific matter, although for most other reasons I'd go youtube. (In general for promotion, seems best, might help your product better, and so, non directly bring money.)