1) We have many large corporations using IPB. One example is NBC, nearly 4 million posts and 260,000 users: http://boards.nbc.com/nbc/. The software is fully capable of handling sites of that size assuming your hardware is. As for search, one of the other developers can tell you more, I'm sure. I believe we recommend installing Sphinx for large sites, which IPB supports out of the box.
2) Our template system works in much the same way, but is also incredibly flexible. As you're probably used to, data is passed into individual templates, and you then use HTML to display them however you wish. The IPB template system also allows you to embed PHP if you want to do advanced manipulation, call templates into other templates if you want to easily reuse content, and even create your own template tags with a simple PHP config file (examples of tags included by default are a zebra striping tag for tables, and a date formatting tag).
Although many boards choose to keep the overall general 'look' of the default skin, with a little effort it is possible to completely change the appearance of the product, with nothing other than template modifications. To give you some idea, take a look at Skype's forum: http://forum.skype.com/ Although their live forum is running 2.x, their skin has been created for 3.x with zero backend modifications. It's all templates :)
The best way to see for yourself how the templates work is to try the demo, just go to http://www.invisionpower.com and click the Sign Up button on the homepage for a private demo installation :)