No do not do this.

Which version do you want to keep? You will need to look at the data to determine which version is the most linked to. Than just redirect www to non www or vice versa.  You should also setup both non www and www versions of Google webmaster tools.

Also in the version you want to keep, go to your google webmaster tools>configuration>settings and than define which version yo want.

Disvow tool should be considered the last resource for removing links to your site that are shady.

All depends how you can categorize them. I have done/worked on sites that are more than 2 clicks and they do just fine with revenue.

Do the 20 categories have any parent categories you can put them into to put in the navigation? Also what about drop down navigation. This can allow them to dive deeper if they want or browse if they need to.

Can you give me some examples or a screenshot?

How are your permalinks setup? Posts typically have a dated url structure which could add to their freshness for the site. It is also argued one of the things you should do with post permalinks is move away from that url structure if you want your post urls to rank for a period of time.

Outside of that it really has to do with the site. Are posts given any better visibility from an internal linking standpoint? Are their technical aspects different? title tags, h1 tags etc?

You need to write out every different aspect down and start thinking of what it can be.