Cache problem with page and file selectors

Maybe can anybody help me?
I have strange problem. I think this problem connected to caching. If redactor try to add thumbnail to a page, file selector choose not file selected this time, but file selected previous time. Clean cache 10 times and more doesn't help, turn off cache nether. After few days I can add new thumbnail to a page, but only to one page. If I try to change selected image and pick another image it doesn't changed. The same problem with sitemap selector. It seems in javascript store cID or fID and nothing can clear it. I have enable pagespeed plugin. It works with 2 other sites in the same server - 5.7.13 and 5.8.1. Other site works normal. I clear and pagespeed cache, it doesn't help. See screenshots. There I choose an arm-chaire, but file-manager show a mirror, which I choose before. I tried to find problems for one month without success.

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MrKDilkington replied on at Permalink Reply
Hi theana27,

I would try disabling the PageSpeed plugin and check for other caching that might be enabled. The other sites on the same server may work because they are using different settings.
theana27 replied on at Permalink Reply
Hi. Thank you for your answer. But I am sure that all sites have same setting, because pagespeed automatically set caching for all sites and I didn't make any changes for this site. Besides I made backup and test now on other domain on the same server. This server VHS and I am admin. The second site from backup doesn't have this problem.
Any way I will try disable pagespeed.
hutman replied on at Permalink Reply
Does your host by chance have Varnish caching on for one site and not the other? I've seen some strange things when that's enabled.
theana27 replied on at Permalink Reply
Yes, you are right. Page-Speed made this problems. Anyway it's strange. I use it before this problem starts. I tried several times enable with different configuration - nothing helps. I saw in pagespeed cache directory that it was cached ccm directory and index.php?ccm..
When I add this

pagespeed Disallow "*/ccm/*";
pagespeed Disallow "*/index.php*";

everything start works.
Thank you for help.