It's faster than comparitively it used to be, it's not faster than raw HTTP, but it isn't far off (excluding negotiating the initial connection). If you're talking about people using SPDY rather than just plain HTTPS, then that's a different matter as well.
That being said, I am not advocating against using HTTPS all the time, I think that would be fine.
You need to answer a few more questions for the best help here.
What's your technology stack (ie. Apache, or nginx + php-fpm, for example)? 2GB RAM also seems awfully low for an 8 core Xeon, however that's not to say it should have any problems running a decent sized IPB installation.
How large is your board, how many posts, topics and concurrent users in general?
It heavily depends on the size of your actual posts as well. Larger ones obviously take longer to convert. We have around 5 million and a beefy server and the normal script for us would have been more than 48 hours of solid run time (I stopped running it after about 24 hours straight).
If you have a large board it may be worth checking out my converter for doing this. I should note that it's completely unofficial but has positive reviews from those who have tried it and can leverage parallel processing on your linux server to speed things up.
Yes in your config you should set that to "utf8", although I believe it's supposed to default to that anyway. There should definitely be an error in your log due to the fact that IPB is reporting an error. You should try to load the website, then check cache/sql_error_latest.cgi or whatever it's called.
Sorry for the slow response, you are correct, Linux is a requirement for this script. It would be possible to make it run single threaded but ultimately you may as well just run bfarber's script, I am about to issue a patched version of this though which uses a superior third party library for UTF-8 encoding.