Custom Field Template -> No issues noted.
Google Analyticator -> No issues noted.
Google XML Sitemaps -> no issues noted. Even had it build an XML sitemap. Nifty plugin.
Redirection -> No issues noted.
Search & Replace -> No issues noted.
W3 Total Cache -> No issues noted. Again, neat plugin, might have to play around with this one a bit more.
Yet Another Related Posts Plugin -> No issues noted.
In case your wondering, basically I installed each plugin, activated, quickly viewed a few site pages and admin pages, maybe tinkered a couple of settings, and tried to spot if anything broke.
The only one of the plugins you listed I noted anything was with the "All in One SEO Pack" which spat out a couple of errors and garbled output on one of the admin pages, but nothing visible to the "external" user.
I also deactivated the plugins to see if this had any adverse effects, and didn't come across any.
Keep in mind: I have a fairly straightforward theme, nothing JAX-y to get in the way or create conflicts. Also, I didn't have more than 3 of your plugins active at any one time. Your mileage may vary.
Also, good on you for testing on a duplicate site, it's really the only way to be sure that nothing is going to cause you grief. I have other plugins which might have inadvertently prevented errors from happening, although usually it's the other way around - too many plugins can conflict with each other.
Have a good night!