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Mostly no on iFrames, or not in a reliable way. Redirect 303 is more uncommon, but similar to a 302. Either one is not the way to permanently send old content to new. Google has a guide on redirection here: https://support.google.com/webmasters/answer/93633, and iFrames here: https://support.google.com/webmasters/answer/34445.  Cheers!

First thing: Your sites authority will not decrease because you add an external link (otherwise no one would ever link) Second thing: Exactly how much is passed is a little hard to determine and is not revealed by Moz, someone asked a similar question earlier this month and this has got some great responses and I don't want to duplicate their work http://moz.com/community/q/how-much-domain-authority-is-passed-on-through-a-link-from-a-page-with-low-authority Thanks Andy

Nothing, in my opinion it´s good. Creating backlinks in a new website is not a good idea IMO! Wait at least 1 month and be sure to have content/indexed urls before starting with the link building campain

I personally have done with with floridagunclassifieds.com i immediately saw the benefits from it. My key words were all in the domain. The expired domain was around since 2001 so I got the benefit of having an already indexed domain from google. It took about 4-6 months off my SEO time table by using the expired domain and building it up. I am now #3 in florida for my keyword and quickly climbing the rankings.. Go ahead and use the new domain!