1. Currently, LinkedIn isn't one of the options for sharing. However, as you mentioned, you can copy the link to share it there. Since there are many social media providers out there, I don't think every single one can be supported. The supported ones include Google+, Facebook and Twitter which are the major social media providers.

 As mentioned, there [aren't a lot of people sharing on LinkedIn][1].

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2. Yes, if you are sharing directly, you will earn the badge. However, you must use the link from the 'Share' button as it includes your userid.

 (share link) `https://meta.stackexchange.com/q/289248/327561` (327561 is the userid).

 (normal link) `https://meta.stackexchange.com/questions/289248` (This won't work)


  [1]: https://meta.stackexchange.com/questions/116730/why-cant-we-share-on-linkedin-anymore/116732#116732