It has more recently been the case that your site can receive an SEO boost from improved page load speeds. There are a number of elements here that may require sorting out.
Perhaps the quickest thing to do is to upgrade you web server. This is not the best thing to do, but it is the lowest effort. A SSD hosting package will decrease loading times of you webpages and hopefully help with your SEO.
Site Ground are a good hosting company that offer SSD hosting for not much money. For the environmentally conscious why not try Green Geeks.
You may need to compress the images on you pages, if the file sizes are large this will slow down the page load speed.
A good way to update pages automatically, which can help with content requirements, is to use a RSS feed to HYML convertor (by example) but this can create problems, as this "resource" may fail to load and add to your page load speed times.
Just as a page might wait to load a script, it may also wait to load a linked CSS file. Get around this by putting you CSS in line (ie on each page). We dont normally do this but it is a trick you can use. CSS Tricks is a great website.
Remember Google Plus One? That's gone now. But the code for the plus one button might still be on your webpages, hidden back stage in the code. Similarly we find all sorts of derelict code, buried in the bowls of websites, sometimes masses of it. One old site we looked at was comprised of around 90% redundant code, left over from some old menus that were no longer used.