Hi there,
The internet is vast but the odds are extremely low you will find someone here who specifically interviewed with Kearney in Slovenia in the past few months.
1. The office in general (number of ppl, markets they cover - I assume the Adriatic?)
This is exactly what networking is for! Get on the phone and talk to some people there. I can't share links (blocked), but go to the Kearney website and find their Slovenia office page.
2. The typical interview process for this office (I assume 1st round 1 case and fit, 2nd round 2 cases. Any tests to be aware of)?
Generally 2 rounds with a combination of fit + case. Try not to have set expectations but rather be flexible. If there is an assessment, then will tell you (though there should not be)
3. What are the Slovanian office typical cases? What do they specialize in? (i know Kearney specializes in operations, procurement, supply chain, but I wonder if it differs for the Slovenian office / Adriatic region)
No such thing as “typical office cases”. Again, go to their website to understand their major industries/functions and that will give you an indication of higher odds of case types. However, please don't go in expecting any one specific thing - it could be anything!
Here's some reading on how to prep in general cases: https://www.preplounge.com/en/articles/how-to-shift-your-mindset-to-ace-the-case
And prep on fit: https://www.preplounge.com/en/articles/tell-me-about-yourself-interview-question
(edited)