Are all matching indexes (indices) searched for a query? If I have multiple indexes that include a common attribute - will each index be searched upon a query involving this attribute? Or is only one index searched?
It depends very much on the DBMS being used. Some can never user more than one index per table and query other can do so.

But if there are multiple indexes sharing the same column, I doubt that even the DBMS that can use more than one index would do it, especially if the leading columns are identical. 

If there is an index on (foo)  and one on (foo, bar) the first one is redundant as every query that would benefit from it could also use the second one.

I highly recommend the site "Use the index Luke", it has a lot of in-depth information about how indexes work and how they are used including the differences for most of the popular DBMS