>If a user has USE TABLE in 0 Shared and indexes on NAME, will this affect the speed on another user that shares this table and indexes on CITY? In other words, does the second user has to wait until the first users finishes his index or using the table?

The user will need to have the table EXCLUSIVE to create an index unless the index is local. In this case, it will take longer for user two to create the index, but he won't have to wait for user one before creating the index.