Are there any problems with caching and certain Joomla plugins that require regular updates like twitter feeds?
Generally, caching should not affect social media extensions. Unfortunately, sometimes feeds are not properly displayed because the cache plugin loads the data from the cache. To avoid such issues reposition the system cache plugin and make sure that it is loaded after the social media extensions.
How expensive is enabling or creating a Reverse Proxy Server setup?
There are free reverse proxy products such as Varnish and Nginx. However, the installation and configuration is usually the most difficult part. If you hire a professional System Administrator to do this for you then a similar project could become very expensive. Supporting a Joomla! website which uses a reverse proxy is also expensive. For example, Varnish developers offer paid support and the basic plan starts from 10 000 EUR. Thus, my advice is to find a web host that already uses a preconfigured Joomla! reverse proxy setup.
How do these optimizations work with the Gantry Framework? Any issues?
Is gantry a particularly slow framework or could you recommend a better one for building a responsive site with Joomla! 3?
I am using a paid template with a template Framework that comes with extra Cache System. Should I use the templates system or the Joomla built-in one?
If your template has its own cache system then my advice is to use it. However, this doesn’t mean that the Joomla! cache should be disabled. Both can work together and in most of the cases this setup will speed up your site even more.