Why continuity requires bluetooth? Why can't the Continuity feature use only wifi, or even only the Internet? As I understand it requires Bluetooth 4.0 and doesn't work without it. Why? Is it for communication between OS X and iOS? If so, why it's not using other available communication channels, such as wifi or the Internet?

If it is because of security reasons, I don't understand how Bluetooth is more secure than SSL, for example. Or there are some other reasons for requiring Bluetooth?
Features like Handoff and instant hotspot need a reliable way to tell when the devices are close to each other.  Being on the same network doesn't really mean anything and determining distance from Wi-Fi signal strength is very iffy.

BT 4.0 has a proximity profile that allows devices to tell when they are near each other and even how far.  Furthermore it does that by sending and receiving very small packets to broadcast and read the devices characteristics.

To further clarify, Handoff and Instant Hotspot use BT to allow the devices to sense each other's proximity, but the actual document and data communications are over TCP/IP.  Here's a discussion on why that is:

http://www.dslreports.com/forum/r29619197-Yosemite-maximum-distance-for-continuity-

And here is a conceptual explanation (from an iOS dev point of view) of how Handoff works:

https://developer.apple.com/library/ios/documentation/UserExperience/Conceptual/Handoff/HandoffFundamentals/HandoffFundamentals.html#

This is where BT comes in:

"Handoff passes only enough information between the devices to describe the activity itself, while larger-scale data synchronization is handled through iCloud."