Google ranks your site(s) based on various factors, but the most important ones are:
a) Original content (obviously)
b) How well your HTML is structured, in other words, how easily crawl-able it is. If you enabled Google Structured Data (GSD) in the SEO tab of K2's Settings, this significantly helps.
c) Performance, how fast your site loads, both server-side and client-side.

Regarding your specific examples, if you search using a private window (so the results are not filtered by your browsing preferences) for this www.google.com/search?q=%CE%9F%CE%B9+%CF%80%CE%B9%CE%BF+%CF%80%CE%BF%CE%BB%CF%8D%CE%BD%CE%B5%CE%BA%CF%81%CE%B5%CF%82+%CE%AD%CE%BD%CE%BF%CF%80%CE%BB%CE%B5%CF%82+%CE%B5%CF%80%CE%B9%CE%B8%CE%AD%CF%83%CE%B5%CE%B9%CF%82+%CF%84%CF%89%CE%BD+%CF%84%CE%B5%CE%BB%CE%B5%CF%85%CF%84%CE%B1%CE%AF%CF%89%CE%BD+30+%CE%B5%CF%84%CF%8E%CE%BD+%CF%83%CF%84%CE%B9%CF%82+%CE%97%CE%A0%CE%91 your site comes up on the 4th page and it links to the first page of the category "ΕΠΙΘΕΣΕΙΣ": adapokrites.gr/kosmos/eidiseis/nea/%CE%95%CE%A0%CE%99%CE%98%CE%95%CE%A3%CE%95%CE%99%CE%A3

Which seems normal. A category page can be more popular than an item page.

If you want to be more specific, you need to use double quotes surrounding an item title, e.g.: www.google.com/search?q=%22%CE%9E%CE%B5%CE%BA%CE%B1%CF%81%CE%B4%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE+%CE%B5%CF%80%CE%AF%CE%B8%CE%B5%CF%83%CE%B7+%CE%BC%CE%B1%CF%8A%CE%BC%CE%BF%CF%8D%CF%82+%CF%83%CE%B5+%CE%B1%CE%BD%CF%85%CF%80%CE%BF%CF%88%CE%AF%CE%B1%CF%83%CF%84%CE%BF+%CF%80%CE%B5%CF%81%CE%B1%CF%83%CF%84%CE%B9%CE%BA%CF%8C%22&oq=%22%CE%9E%CE%B5%CE%BA%CE%B1%CF%81%CE%B4%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE+%CE%B5%CF%80%CE%AF%CE%B8%CE%B5%CF%83%CE%B7+%CE%BC%CE%B1%CF%8A%CE%BC%CE%BF%CF%8D%CF%82+%CF%83%CE%B5+%CE%B1%CE%BD%CF%85%CF%80%CE%BF%CF%88%CE%AF%CE%B1%CF%83%CF%84%CE%BF+%CF%80%CE%B5%CF%81%CE%B1%CF%83%CF%84%CE%B9%CE%BA%CF%8C%22

This will reveal your site in the 1st page of results, as 3rd result (direct URL to the item). Which is also normal (being 3rd), because the given item's title resembles that of other higher-ranked sites compared to yours (this usually indicates content that is not the source).

So all in all, I don't see any issues in regards to content crawling, for a site that may have not used GSD in the past. I see it's now enabled though which is a plus.

Additionally, make sure you add your site to the Google Search Console so you can monitor crawling issues.

If you can't do anything about the site's server-side performance (I see it's on Plesk with Nginx as proxy to Apache - which probably doesn't really do much unless you cache a few things on Nginx's side), you should:
a) focus on well structured menus and content (your HTML)
b) enforce tag normalization (e.g. make all tags lowercase or uppercase by default, regardless of what editors input as tags) to avoid duplicate tags because the case is different
c) do the trick I've mentioned before in this forum to enforce all tag, user and other links that are autogenerated to be mapped to a "root" K2 URL. If you don't already have such a menu item for K2 (one that points to all K2 categories), create one in a hidden menu and give it a generic alias (e.g. "content"). Then in the SEO settings of K2 enable "Advanced SEF URLs", clear your caches and check e.g. your tag URLs.

Also keep in mind that K2 will create duplicate tag URLs because this is how Joomla's URL router works by default.

Try the above and let me know.

If you need performance or other consulting, you can always use the contact form to get in touch with me directly.

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