Dear Denis,
The reason for the special characters displaying oddly was that the Latin Extended character set was not included into the @font declaration. Some Google Fonts, like e.g. Open Sans which is used as the body font on your website, do support special Latin characters like č, ž, and so forth, yet one needs to include this set into the code: when you pick a font on Google Fonts by clicking “Quick-use”, you’ll be given several options before the final code is generated: the first one being font styles, and the second one being the character sets; if you mark “Latin Extended”, you can see that the generated code is changing to incorporate the new set. Now, if you take everything between “family=” and the closing single-quote, and place it into the Theme Options, “Typography” tab, as I did for you for the body font, you will have all styles and the extended lating characters displayed correctly. Note, however, that the heading font, Coda, does not support Extended Latin character set, which is why I’d recommend changing it to Open Sans or any other font that does (you can filter fonts by supported character sets in the “Script” drop-down on the Google Fonts home page).
Also, a side note: I strongly discourage from using the WP Super Cache plugin on development websites – it tends to cache too often and can obscur coding/styling results. I’ve switched off the plugin to check if my font fix is working (and it seems that it does), and I recommend switching it on only after you’ve finished with the production stage for the website.
Another small thing – I’ve added an extra CSS styling line to fix the appearance of the e-mail subscription widget ;)
Sincerely,
Andrew | Satori Studio