Yes, it requires additional hardware to program a new PIC (as indicated in the manual). PICkit is one such with good features for the price, including debugging, serial communication and logging. Once you have a way to program your PIC, it can communicate through the serial port; this could be used to implement a bootloader in self programming capable chips, the way boards like Arduino work. Your Loginway PIC-01 is a pretty good host board to build on, and certainly more featureful than the host board in the PICkit bundle.
You are parasitically powering your IC through the protection diodes on the Rx IO line.
I'm assuming you have voltage on the Rx line (presumably 3.3V or 5V). This is getting into the PIC Vcc through the protection diodes on the IO pins.
From the PIC18F2550 datasheet:
I/O pins have diode protection to VDD and VSS.
There's not much you can do about this, and having any current flow through the protection diodes is a bad idea (they're not intended for this). You will have to modify your circuit to prevent voltage from being present on any of the PIC pins when the PIC is not powered.
If you can't prevent voltage from being present on the PIC IO lines when it's unpowered, you should clamp the Rx line to Vcc and Gnd with shottky diodes. Since the diodes in the PIC are constructed on the silicon die in the MCU, they are plain-old silicon diodes, with a \$V_{F}\$ of ~0.6v. Since the clamp diodes are schottky, they will begin conducting before the internal diodes on the PIC, so the MCU will be safe.
Of course, if the source driving the Rx line can source enough current to power your whole circuit, you'll wind up simply powering your circuit this way. To compensate you'll need to add a series resistor inline with the Rx line.
Best Answer
I can't tell exactly what you are looking for, but we sell both PIC development boards and programmers. Take a look at our products page.
The ReadyBoard series is meant to make it easy for you to implement your own circuit around a PIC. The board provides the basic infrastructure, like power supplies, RS-232 interface, reset control, debug LEDs, etc, but doesn't try to include "peripherals" as such since every project is different. Instead we include a large breadboard area where you can add your own circuit that does just what you need.
The ReadyBoard-02 is targeted to USB applications and therefore comes with a 18F2550, but it is compatible with any 16F and 18F in the 28 pin DIP footprint. Note that this is different from the PIC 24, 30, 32, and 33 28-pin footprint.