If the Giant's power and/or toughness change so that its toughness is less than its power, you can have the ability target the Giant itself.
To work as an evasion ability, an attacking creature must already have flying when the declare blockers step begins. Once a creature has become blocked, giving it flying won't change that.
If Stone Giant's ability is activated during a turn's end step, the delayed triggered ability won't trigger until the beginning of the next turn's end step. The targeted creature will be destroyed at that time.
When the delayed triggered ability resolves, the targeted creature is destroyed, even if it's no longer a creature, no longer under your control, or no longer has toughness less than Stone Giant's power at that time.