Benefits of social sharing

You might want to take a look at how http://support.lampcms.com awards reputations to users who share.

Yes. this is one of the ways that users can be encouraged to share content. This helps the popularity of the site as well

If it's going to be implemented here, a good place to place the social icons is at the bottom of the question, that is, just before the first answer. That way it will be give more room to show how many points users earn by posting to each social network. Kinda the way LampCMS has it. The only difference will be in the position.

How would you prove that the tweet/share on facebook was actually posted? You can sure detect the click on any of those icons, but that alone will be a way to game the reputation system since you can always cancel the sharing process.

I'm not sure if this even makes sense, but isn't there a way to track pingbacks to a question in much the same way as is done with blog articles. Just throwing out an idea, so if it doesn't make sense, just ignore it.