How to use international experiences for a US faculty position?
I've had some experience in interviewing candidates from other countries, although my department has never hired a candidate who was not already working in the US.  

The first thing to consider is what kind of position you're applying for.  It sounds as though you are not a relatively new PhD but rather that you have 10 or more years of experience as an academic in another country.  

In practice, most academic positions in the US are openings at the assistant professor level, and most candidates for these positions will be recent PhDs (say within the last 5 years) with some post-doc experience but no experience in a tenure track faculty position.  It is not very usual for a more experienced faculty member from another university to be appointed to such a position.  Most universities would prefer to hire a new graduate from a top tier program with a couple of years of post-doc experience and then have that faculty member develop as an assistant professor at their institution.  

Some positions are advertised at the "assistant or associate professor level", and you would be a better candidate for such a position.  In these searches, the committee is typically trying to hire the highest quality candidate that they can find, and a more experienced candidate with a good CV can be competitive.  On the research side you will need to demonstrate that you have been consistently productive throughout your academic career.   This means that you've been regularly publishing in good international journals and have published at a high rate.  A post-doc who has published 12 papers in two years in good journals will look better for this kind of position than someone who has published 80 papers over a 20 year career, particularly if not all of these publications were in top journals.  It is also important to have teaching experience in English (be sure to mention this in your CV and cover letter.)  

At the full professor level the department is often looking for a distinguished researcher to fill a named professorship and/or lead a research group within the department.  Unless you're one of the top experts in your field, you're not likely to be competitive for such a position.  Often these kinds of positions are filled by recruiting a faculty member away from another university by offering them a higher salary, special facilities, and the opportunity to hire assistant professors in their area.  

You might also consider applying for a department chair position.  These are typically part time (varying to essentially full time) administrative positions with some expectation of teaching and research.  The ways in which public and private universities in the US are funded are very different from other countries and their are many differences in university administration that might be challenging to someone coming in from another country.  

There are of course immigration issues to consider as well.  Most of the more prestigious universities are generally willing to pay the costs associated with sponsoring a tenure track faculty member for a visa and ultimately permanent residency.  However, some lesser ranked institutions will balk at the cost.  

In answer to your specific questions:


  How do search committees compare local and international candidates?


Your research accomplishments should include conference presentations and publications in international venues.  Publications in journals that are local to your country or continent will not receive much credit.  


  Do they care about my unique experiences? for example possibility for
  building collaboration with my home country or attracting
  international students?


In my experience this is a relatively minor factor.


  Are my administrative experiences beneficial or it is a faculty
  position and nobody cares about administrative works?


Only if you're applying for an administrative position such as department chair.