Better you go with wp super cache plugin for live site. I hope it will work for you.
And then installing-a-local-server with XAMPP
Install in other than C drive in your system. Maintain a separate drive completely for development purpose. Installing in C drive, where all our programs installed, might reduce the performance in your system. I always prefer to allocate separate drive (say D or F etc.) for development. So, if you like to format your system in future on various reasons, you need not worry about your previous installed directories or sites present in other than C drive. And install notepad++ along with XAMPP.
Now test your database along with your current working theme. Do several tests on test site(s) at your local server. If you succeeded to resolve your present or future(likely to face) issues, then you can implement that in your live site. And you should keep your live site clone at your local server too, as a part of all other test sites in your local server.
I always suggest install multiple sites in your local server for various development purposes. I do follow these steps before going to implement in live site.
Test_Site1: A clone for your live site as a separate development site (do not test every thing here). It gives you greater control if your live site being hacked or facing zero day vulnerability.
Test_site2: This is for testing the cloned site, after u resolve your issue here, implement in test site1.
Test_Site3: This is for testing the compatibility, or to verify various plugins or themes functionality etc.. In this Test_Site3 you need not upload all your database. Just for testing various feature that are likely to be implemented in future.
Test_Site4: If you would like to develop themes, plugins etc. then can do all that stuff here
After every thing is in your way from Test_Site3 to Test_Site1, then you can, no doubt, implement the same to the live site.
my wordpress 3.8 and as far as I see there is Twenty Fourteen
No need to worry you can test with that too.
I strongly recommend that don’t try to test on live sites. And W3TC cache plugin is not good for sites under development.
If you want further information on local server installation, XAMPP etc. better create a new thread at relevant place, u get members support for that too.
I hope only site_maps issues with WordPress SEO plugin will be discussed here, as it should serve the purpose of WordPress.Org support forum. Since your theme, most probably, having compatibility issues, unless until you confirm that Yoast SEO plugin is not compatible with other best themes available in wordpress.org, we can do nothing further. So first try your database along with wordpress.org popular themes, then you can get final root cause for all the issues.
Have a nice day
