The establishment clause would prevent

a church from being built in a Jewish area
the mayor’s office from displaying a cross
a citizen from placing a religious scene in a business
the president from having a Christmas party at home

The establishment clause of the First Amendment prohibits the government from establishing or endorsing a particular religion. Based on this understanding, the establishment clause would prevent the mayor’s office from displaying a cross, as it would be seen as a government endorsement of Christianity. Similarly, the president from having a Christmas party at home would not be affected by the establishment clause since it is a personal event and not a government-sponsored or endorsed religious activity.

However, the establishment clause does not restrict individuals' right to practice their religion or display religious scenes in private establishments or businesses. Therefore, a citizen would not be prevented from placing a religious scene in a business, as long as it is not supported or endorsed by the government. Similarly, the establishment clause would not prevent a church from being built in a Jewish area since it does not involve government establishment or endorsement of religion.