Does no mob griefing stop creepers from destroying blocks?

Usually yes. The setting generally prevents creeper explosions from damaging terrain, although the creeper can still explode and hurt nearby players or entities.

Are mobs disabled on a no mob griefing server?

No. Mob spawning and combat usually continue. The rule mainly limits mobs changing blocks or affecting the environment.

Does no mob griefing protect my builds everywhere?

Only from the mob behaviors covered by the server's rule and version. It may not replace player protection, claims, rollback tools, or other region safeguards.

Can no mob griefing affect farms or villager behavior?

It can affect some mob interactions with blocks and crops, so farming and villager mechanics may differ. Check the server's edition and specific rule configuration if automated farms matter to you.