Can a hobbyist or individual apply for Apple's MFi program?

Yes, smaller groups can apply to be in the MFi program, if they are serious about making a product for the iOS devices. However, you will need to get approval from Apple for your basic device concept in order to get in the program, then the device will need to pass third-party certifications to verify that it won't interfere with the iOS device, etc. Finally, Apple will need to approve your final product design before you can start selling it.

They've opened up this process significantly over the last year or so, but given the hurdles you have to jump to get a functional device out there this is still not intended for one-off hobby projects. A small company can make a product to sell in lower volumes, but you'll need at least $20,000 in development funds to get through the process to your final design.

Recouping that level of investment doesn't require selling millions of devices, but you do have to have some moderate volume of device sales to make it worth your initial development time and money.

We're in the process of building an MFi accessory, and we're a very small company. Our target sales volumes are not large, but they're enough to make this worthwhile. If the product takes off, so much the better.

You certainly can, but you probably have to pay the same as if you were a big company planning on selling millions of products.

A friend of mine tried to make a dock-connector-compatible sensor for a college project: Apple wanted to charge him the full corporate entry price to get the pinouts and size specs for the dock connector and the API headers so they could write an app that used it.

However, this is definitely a case of "it can't hurt to ask". Maybe you'll get break if you can assure them you won't be selling it.

You can't. I've tried this route and I got a call saying that you need to own (or work for) an electronics factory to be granted MFi membership. Software companies aren't eligible.