#3: As achievments are not chores, suggestions should be actual goals such as:
Mine a diamond
Craft a golden item
Die of suffocation
Dye a sheep
Craft a painting
Kill a Zombie Pigman
Reel in a Ghast
Kill a spider, and its skeleton jockey.
and finally, #4:
Achievements are fun little goals to complete. They should not increase your "skill", they should not make you mine faster, they are simple mini-quests.
Although achievement rewards (Such as a special cape for very very difficult ones) might be interesting.