Fix Redirection and webmaster tool update

We need a couple of redirection done on our site as listed in 1-3 below and we need answer on the 4 question below. 1. We changed domain name and we did a 301. However, there is an issue within google webmaster tools. It recognises our old domain without the prefix www when we did redirection, but it said we should confirm the same domain with www as it couldnt reach it. We removed the 301 and confirmed domain with www and it accepted it, by the time we added 301 again, google webmaster did not recognises the domain with www because it couldnt reach it, it said it couldnt reach it and we should reverify it. A sort of a minor conflicts i suppose. 2. Find the controller/handler of error and update it to redirect to a specific page if page is not found. We have some pages on our sites that are no longer available or even pages that do not exist. Such as you typing [login to view URL] , i want all of this pages to be redirected to a specific page. 3. We have several duplicate homepage according to this tool. [login to view URL] , all of this various home pages should be redirected to the specific error page mentioned in 2 above. [login to view URL] [login to view URL] [login to view URL] 4. I will like you to explain why we saw a spike in traffic on our site when we change the domain name and did a 301 redirect, even though the new domain does not have any backlinks. The traffic was like x10 our standard traffic and this lasted for like 1 week. How can we ensure this traffic continues to build up like this. I would like your input based on wealth of experience on this matter