@schoolboy,
Thank you very much again,
Yes, I certainly know that I am in "good hands" if Andrew takes care about this issue :)
Code:
 1, Mobile Responsiveness - sites that are not compliant with mobile efficiency factors are starting to drop down the rankings - not because Google drops them down, but because your competitors are Improving their sites faster than you are. They are "leap-frogging" you and this is the major cause of steady falls in SE ranking.
2. Pagespeed. The faster your site loads, the better the search engines (and customers) like it. Faster sites will get more favourable ranking than slower sites.
3. Structured data markup. While this is not yet having a major impact on results ranking, the use of structured data makes your content more "understandable" to google and it will know how to place your links into search results that are more relevant to the search terms a person uses. In many cases, it may appear you are climbing the rankings, but the reality is that competitors are falling lower - you are now doing the leap-frogging.

To me, these three issues are amongst the more important, so we focus on getting the site's software to comply with what is now expected by Google.
1. Mobile Responsiveness: I am checking now every page, (the site is in 6 languages...). It takes some time, but as anyway there are not sales, I have plenty of time.
2. Page speed: I am using a free site, panda, for minimizing the pictures in each page. This is the only thing that I can do. I know that the cache size has influence too, but I assume (?) that it is optimized by the "Fiverr Guy". However, as I suspect, one of the problems is resizing pictures to thumbnails. Most of my pictures are 500px X 500PX. Most thumbnails are 80px X 80px... there are also other sizes. I assume that it influences the page speed too.
3. Structured data markup: here is a problem named... IGNORANCE I read this term several times, googled for it, but it is still unclear to me, especially how to do it in practice, especially in the 6 languages.

BTW, another "Fiverr" tried to insert the "hreflang". Don't even ask what mess it did after inserting it... It took a month or more to "clean" it. Nothing worked, so I gave up using it... even that I know it could help somehow.

One more issue is my main page "animated gif". I have used to use an swf file, but couldn't make it mobile responsive. I tried the "marquee" trick - and it was a total fiasco. However, I know that it is an issue - it is relative big - but I am trying to find a better solution, without any success.

Many thanks again!