Yes, the hardware most definitely is able to act as a HID, Mass Storage or almost any type of USB device. Currently, Teensyduino only adds files to Arduino for a serial type device. I intend to add other types. However, the Arduino IDE contains a lot of serial-only assumptions, so support non-serial device types on Arduino is going to take a lot of work. I am working on that....
You most certainly can use the serial at the same time as the USB. It's like having 2 serial ports. Or a HID and serial, if you program the USB to act as HID.
Teensyduino only supports the Teensy. If you have a usbkey board, Dean Camera's LUFA library, win-avr, and Atmel's FLIP tool are your best option.
Please understand that this project is very new and the website and supporting files are still under development, and Teensyduino (the software add-on for the Arduino IDE) is only in its very first beta test right now. A full schematic will be added soon. Many more examples are also planned. It is a lot of work, as so many people have said dismissively regarding the possibility of using this chip with Arduino. I'm working on a giant TO-DO list.
However, the bootloader is not open source. If you are looking for a 100% pure open source project, including bootloader source code and CAD files under a share-alike license, Teensy is not for you. It is most certainly NOT my intention to deceive anyone. Building excellent web pages is an iterative process, and the teensyduino page has already been revised substantially based on feedback from many people. Please if you have any constructive and specific suggestions, contact me directly at firstname.lastname@example.org
All code that becomes part of your program is open source. Everything I have added is under the MIT license, which is more permissive than the LGPL which Arduino uses. Of course the additions to the Arduino IDE are open source under the GPL, and they are placed in a "src" directory when you run the Teensyduino installer. The IDE changes have also been offered to the Arduino developer list.
About the PWM, while Atmel's datasheet says there are 5 PWM, and indeed there are inside the chip. Unfortunately Atmel decided to put 2 of them on the same pin! The web page says 4 because you can never actually use all 5. I wouldn't want anyone to buy the board or plan their project around 5 PWM outputs and later discover you can only use 4.