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I agree with Andy - it's not all about the domain authority and one day their sites may gain in DA anyway.

Just don't go for any spam links.

This may help: http://lifehacker.com/how-to-auto-post-to-facebook-or-twitter-from-google-wi-1352124886

Not tried it though as I prefer to post to each independently so that the content is tailored.

I would use the main .com domain for the reasons already stated.

It would be helpful to have the landing page look like the design of the rest of the site so I would look at adjusting the design which you say currently doesn't match.

He's a she! And yes that's what I meant