Yes, but you have a problem with your event, no valid date !

Add first a valid date

Yes, your problem is a page encoding somewhere.

Or a php version ! (which php version are you using ?)

iCagenda is using strings of translation from Joomla core ini files.

I see a difference between my template (with Russian date working fine) and your template:

Yours:
Mine:
Maybe the missing dir="ltr" or a conflict with facebook opengraphobject...

Does it works with an other template (beez 20 for example )?

Oh, it can be a problem from your module news.

Which module do you use for it ? (so that i can test it)

Many users are using Joomlsocial and iCagenda without problems...

I think about your new module, because of a maybe setting local, which can not work well for Russian.

To have a link to download this module, can help me to test it

Maybe, but it's not a free template, so i won't test it...