Minecraft – Will Zombie Pigmen spawn in a mooshroom biome

No. Hostile mobs don't spawn in peaceful mode and since the mcpe zombie pigmen are hostile they don't spawn on peaceful difficulty. The items still spawn though.

1. Zombie Pigmen aren't supposed to get damaged in daylight, but they do get damaged and will die from sunlight. (Pocket Edition is strange.)

2. Yep, you can still activate the nether reactor on Peaceful mode, which means the giant Netherrack room will still spawn. Although the Zombie Pigmen won't spawn since it's Peaceful mode, the various items that would normally spawn in the room will still spawn.

   The only time you can't activate the nether reactor is in Creative mode.

3. You only need the 4 gold blocks on the bottom of the reactor, which in total will cost you exactly (4 blocks)x(9 gold ingots/block) = 45 gold ingots.

4. If you activate it in Peaceful mode, there's not much to do except run around and collect the random items. But if you're fast enough, you can actually still retrieve the gold blocks you used, before the items start spawning.

   But on the other hand, if you're not on Peaceful, then you'll have to deal with the spawning Zombie Pigmen. The Netherrack room is easily breakable. However, after a short amount of time, the reactor causes the world to enter nighttime, so trying to expose the Zombie Pigmen to sunlight may not be a good idea.

   If you're sure you can handle the Zombie Pigmen, you can go ahead and try to fight them. But otherwise, you can make a quick escape by breaking down the walls, but the items inside will likely despawn at some point.