Yes, but only for codecs supported by Chrome (basically mp4 and the occasional avi). Anything that needs transcoding (or any file with high bitrate/multichan audio) will cause extreme stuttering unless you have a machine with a fairly beefy processor and GPU.

Casting a tab is like using logmein to watch a movie on another computer. Casting either the RAW or the local file directly is like playing something off a NAS

Yes you can do that. The problem is that currently tab projection is limited to 720p.

If anyone knows how to get around this, please reply to this with the solution. Googling for anything Chromecast related gets mostly pop-tech articles.

Yes, it still can, but the app allowed to stream without using the browser, for example from the phone's gallery.