As the first report states:
Understand the recommendations
They are meant to be generic, best practices; not everything will apply to your site.
Rules are sorted in order of impact upon score
Optimizing rules at the top of the list can greatly improve your overall score.
My experience has been that these types of reports almost always make good recommendations, but the effort to implement the fix personally outweighs the benefit, so you have to think about your own needs and fix your problems over blindly following a generic report like this.
So let's tackle some of my thoughts on the items:
This is a good idea. But you're not going to implement this in Joomla.
To do this would require rewriting a lot of core code. Should that be done, maybe. Either way, I would highly doubt that anyone reading this answer will do it for their own site, so you can effectively ignore it.
Serve scaled images
You can manually scale images yourself if you only need them at a smaller size, but I'm not aware of any core way to get resized images at this time. There may be an extension to help with this, but it will likely have quirks. I would recommend looking in to this, since this can definitely increase the page load time and make your site more mobile friendly.
Specify image dimensions
This could also probably help, but I've never seen it have a big effect.
Leverage browser caching
This is a good idea, but is a server configuration for the most part, so it happens outside of Joomla. Ideally, you at least want the browser to be able to cache images, scripts, and stylesheets. These really don't change that often (or if they do, you should rename them or add a
This site explains how to adjust your .htaccess file to enable caching by extension: http://www.siteground.com/tutorials/joomla/joomla-speed.htm. (Note: whether this actually works is dependent on your host.)
Enable gzip compression
You can do this in the Joomla Global Configuration if you like.
What isn't mentioned in that report
I can see in that report that your site took 7.15s to load. That is obviously WAY too slow, hence why you went and ran this report.
What this report can't tell you is what could be holding up your site in delivering the initial file. I ran a waterfall speed test at http://tools.pingdom.com. This doesn't seem to affect your site (initial response was sub 1 second), so you really need to focus on resizing images (and maybe consider having less images or adding more images through ajax so it doesn't slow initial page load).
For others that may look at this answer, I highly recommend using Joomla's debug mode (in global config) to get a list of queries run on a particular page load. This will give you the time that each query took. Optimizing queries is always my first stop in speeding up a site.