No, the big ones can cause some damage. However the baby ones don't do any damage!
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You can find slimes in flat areas at lease 6-7 blocks wide. Or in slime dungeons.
Yes, Slimes are hostile and will attack players on difficulties other than Peaceful (they won't appear at all in that), or Creative Mode.
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.