Yes, Slimes are hostile and will attack players on difficulties other than Peaceful (they won't appear at all in that), or Creative Mode.
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Yes. Slimes are considered hostile mobs, and therefore will not spawn on Peaceful. Switching to Normal or Hard will give you a higher chance of finding one, but Easy still works. Keep in mind, though, that Slimes only spawn on level 40 (40 blocks above Bedrock) or below, and only in around 10% of the chunks. So good luck. Also, Slimes spawn regardless of the lighting, so lighting an area will indirectly increase the chances of getting a slime by reducing other hostile mob spawns. Hope this helped.
You can find slimes in flat areas at lease 6-7 blocks wide. Or in slime dungeons.
Slime balls are only dropped from slimes. Slimes are green, gelatinous and very rare cubes, found far below the ground level.
In the bottom layers of the map or (if you have Weekly Snapshot 12w40a or above) in swamps.
There are 3 different sizes of slimes in minecraft. Big , medium ,and small.