How much server-side resources does the Omega theme use? Is the Omega theme scalable? The omega theme is pretty 'fat'.   Currently its probably the biggest theme on drupal.org.  You can do anything and everything in the GUI. You can completely customize the layout, turn responsive design on/off...I could go on for awhile.

My question is,  do all of the extra settings eat up server resource to serve a page to the client? If I have a website that receive 100,000+ page visits a day,  should I use omega, or create my own theme?
Yes there is some extra overhead involved (especially at the templating level); how much this will effect your response times will completely depend on the setup of your server. An easy test would be to enable the basic Garland theme, profile the site, then enable the Omega based theme and do the same. You should get a pretty good idea of how much extra overhead you're likely to get for a single page load. 

If you're able to, go further. Stress test your server (using something like ab) with both themes enabled. That'll give you an even better idea.

If you've got a site with 100,000+ visitors per day though, your efforts might be better spent setting up a decent caching strategy, both in Drupal and on the web server. That will help to offset a lot of the overhead that Omega/Alpha can add.