Is the world alive?
More alive than any single player game, yeah..
Can I have an impact on the world?
The level of player impact depends mostly on the game. Eve-Online, for instance, is VERY heavily controlled by player corporations. EQ, less so, but it's an older game. The economy is still ultimately controlled by the player.
If I steal this item...
The ability to steal really shouldn't be part of your RPG criteria..
What if I attack this person & kill them .. faction
All MMORPGS have different factions affected by your actions (At least all the ones I have experience with (AC, EQ, DAoC, Eve-online, AC 2, AO)...
The rest of your questions are fairly inane. All persistent worlds require monster regeneration of some sort. Re-spawing is the most effective method. NPC's with character; maybe not as much as a traditional RPG like Baldur's Gate, but this is only because they play such an insignificant role in the game. As for freedom, it is unrivaled in good MMORPGs..
Final note: Make your name less annoyingly long and don't try and redefign the genre of "role playing" based on your apparently limited experience.
I eat pasta!