Until BB supports flash you really can't do either, and so far as I'm aware there aren't any plans to support it in the near future.
That is incorrect. You need to be using the Beta OS 4.5 on your device.
To do this, you must understand the process to install the OS to your BlackBerry and also obtain and illegally leaked copy of the OS. If you are inexperienced with these then I would recommend waiting for the official release in the next couple months!
Also, running a Beta OS may cause bugs on your Berry, etc. Feel free to search the boards on more info regarding the OS 4.5 Beta
I have an 8330 from Sprint with OS 4.3. YouTube vids worked fine for me using the regular browser that comes with the Sprint version of the Curve. I went to the mobile YouTube site.
I'm on Verizon with 4.3 and was able to watch youtube videos with that link too.
Yes, I can also view youtube on my verizon curve with 4.3. The only time I have an issue is if the signal isn't strong, I'll then get a download error, incompatible video format. Just move a little bit for a better signal then no problems.