If your client has an iPhone, then use TestFlight - it makes the whole process of building for ad-hoc distribution much easier and a lot more efficient if you plan on sending multiple builds during development.
You can check them out on http://www.testflightapp.com - They have great getting-started docs and it only takes a few minutes to start the whole process - also, you don't need to install their SDK if you're just sending a pre-release build to somone.
To answer your questions more specifically:
The file that gets exported for iOS development is an .ipa
The .ipa must indeed be signed by an ad-hoc distribution certificate
If you use TestFlight, your client will be able to install your app from an email - super simple!
Oh, and did I mention that it's completely free? :)
EDIT:
As mmc pointed out, you should check out the basics of Ad-Hoc distribution before using TestFlight, just for your own peace of mind. mmc recommended looking at How do you beta test an iphone app?, and an intro to TestFlight can be found in their tutorial base, here.
Source:
http://stackoverflow.com/questions/14035040/exporting-your-ios-app