Once in the past you have been asked whether you want also to share downloaded files (that's why the 36 files). You have agreed to do so, hence any file you download will increase the amount in the oval window.
People sharing personal files might have done so because they haven't read the user manual of LW (as you seem not to have):
http://www.limewire.com/english/content/userguide.shtml
They might have accidentally put their "My Documents" folder on the list of files they wanted to share.

A personal note,.....if your desire for certain files for free is greater than your safety concerns, then you should maybe consider not to participate in P2P filesharing.........especially if you're in the US.

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"Never Argue With An Idiot. They Will Drag You Down To Their Level, Then Beat You With Experience"

I reset everything back to default settings and started from scratch. Now I know how it works. Thanks for the link to the manual!