1. Does a 0 on the Digital Output pin of Atmega8 equivalent to Ground?
Yes, with the proviso that the pin has some output resistance and a current rating of 40mA.
If I connect a LED + Resistor betwen D-Out pins 1 & 2, with Pin 1 outputting '1'
& pin 2 outputting '0', will it light the LED?
Yes, provided the LED is connected the right way round.
If so, is it safe to do so instead of using Ground?
(I read something about considering the sink current & such!)
Yes. That is essentially how multiplexed LED displays are driven.
2. Will the following work?
My aim to control the gradual dimming & brightening of individual LED's.
Yes. Just be sure that you respect the 40mA absolute maximum current per pin limitation (for both the low outputs and the high outputs), and the current limitations per port and per device (e.g. 200mA Vcc or ground current for an atmega328p).