If you have multiple ads running, how do we know which one is doing better for particular keyword.
A- You need to do A/B testing
And what if you have two ads with different domain names and the ads are showing 50% of the time each.
A- unless your an agency you won't have 2 domain names, and even i you do they won't relate toeach other when it comes to analytics. Each domain is a separate campaign.
How do you calculate keyword score?
A- You don't, the SE's do. You can look at CTR but that is your only gauge.
If you pause one ad, would the quality score change for the keywords when you have one domain showing and then change again for the second ad with the second domain? You can see how this is confusing, but important.
Doubtful because again, you will have 2 different campaigns. I have multiple clients i (4 in fact) in the same category. Bids, ctr, landing pages and all the other SEO factors come into play.
 If you try different landing pages from the same domain (say WIDGETS.COM, are they treated exactly the same as far as quality score?
A- No, google looks at your ctr to determine positioning and quality score
Is your entire domain rated, and an landing page, not make much difference? The don't rate your domain, they rate the ctr of the kw as it relates to the landing page.
In other words, to get a better score is it neccessary to put a test landing page on an entirely new domain to get away from a general score that they are rating a whole domain.
You won't be able to drive traffic from 1 adword campaign to 2 different landing pages on different domains.
 Each keyword can be redirected to its own URL.(YES, IF OFF OF THE BASE DOMAIN) Lets say that I have all the keywords going to the default URL in my ad, but one keyword I redirect to either another landing page in the same domain. Would that affect that individual keyword? YES. IF THE CTR IS BETTER THE POSITION WILL BE HIGHER AND THE COST WILL BE LOWER. Or as I stated before is the entire domain rated, and no changes to an individual landing page would make a difference...? NO, THE DOMAIN IS NOT RATED.