How Do I Split Test 2 Domain Names?

By authority, I simply mean the site that you're going to primarily focus on for adding content and building backlinks... I jumped the gun assuming you wanted to pick the perfect domain to build a large following for a business/brand.

There's no set criteria for an authority site vs. a non-authority... authority sites generally have a ton of pages and backlinks with regularly added content, and have been recognized by Google or other SEs as a go to source for information on a particular niche. When a page is added to an authority site it usually ranks well almost instantly.

Non-authority sites are probably easier to understand by thinking of them as minisites, sites from 3-30 pages that are more set and forget and focus on a smaller group of keywords.

Correct. I would at least put an anchor text link in the body of the homepage. So if you wanted your main site to get ranked for "lose weight fast" you would hyperlink that phrase on the smaller site, the hyperlink pointing to the main.

Very important if you're creating your own link juice with a few or many of your own sites. SEs won't give much, if any, credit for you linking to other sites of yours if they know they're all created by the same entity. The easiest way for them to figure that out it is by the IP address of the hosting... if it's the same, they don't dish out the juice (or at least nearly as much.) Some SEO guys have reported actually hurting their rankings when doing so, but that's up for debate.

If you reciprocal link, even with different Class C IPs, between your sites you won't get as much power as just linking one way, which is why if you do this you should pick one of your domains as the primary focus to acquire traffic and rankings.